The Midwestern United States is one of the most geographically well-suited places on Earth for the development of high-speed trains, but the problem is funding the development of the trains themselves. By the time the Shinkansen has had any operational bugs worked out and the TGV is in development (early 1970s), the United States' freight railroads were in serious economic trouble and the country had a very good air travel system. That all being said, I don't think its entirely out of the realm of possibility, but the development of the Pennsylvania Railroad's Metroliners in the late 1960s proved the point was indeed possible.
If you are serious about this, the ideal start point would be to have a speed race in the 1930s between several railroads - this is easy to achieve - the Pennsylvania developed its T1 duplexes, which were capable of 150 mph, for high-speed operations, and its easy to get others to do so as well - with this putting the idea into the mind of the traveling public. The New York Central and Burlington Route get into the battle, resulting in the Denver Zephyr and the 20th Century Limited in the early to mid 1930s having big steam power (diesels are incapable of such speeds with 1930s technology, I think) and operational speeds of better than 120 MPH. The Pennsy T1 and whatever the NYC comes up with (a Challenger-type maybe) blow the Europeans out of the water in terms of steam speeds, with both putting up numbers of better than 150 mph all-out on test runs and further narrowing the schedules of the name trains. Meanwhile, Santa Fe, Union Pacific, Southern Pacific and Great Northern inaugurate their great streamliners, introducing the Super Chief, California Zephyr, City of San Francisco, Empire Builder, Sunset Limited and Coast Daylight into the world of railroading. This by the end of the 1930s has caught America's imagination, and the western streamlined trains soon begin dispensing with their coach cars (or improving them) in favor of coach trains that run similar routes, following the Santa Fe's example with its Super Chief and El Capitan. The Southern US railroads soon follow, with the Southern Crescent, Silver Star and Palmetto the result, and several midwestern railroads make up trains to match up with the top-line streamliners, producing the Golden State, City of New Orleans, North Coast Limited, Rocky Mountain Rocket and others.
After the war, legal changes allow the railroads to charge what they like on the passenger trains for extra fare, allowing the railroads to have the funds to continually improve their services. Out west, luxury trains ruled, with the Super Chief, City of San Francisco and Empire Builder setting the standard by which everyone else is judged. A deal between the Great Northern and Southern Pacific results in the Coast Starlight, a Seattle-San Diego/Los Angeles train which is an instant hit, and the Western Pacific/Rio Grande/Burlington Route California Zephyr is another huge hit owing to the scenic charms of the route. Recognizing the jet age, the trains one by one get new equipment, diesels replacing steam power (usually the EMD E-series or Alco PA locomotives, which were each equipped with twin prime movers) and ever-better equipment. This reduces passenger losses (and even allows profits in some cases), and while some contraction is inevitable, by the late 1950s the trains that do live on being able to prosper based on a clientele that wanted comfort as well as speed, and railroads that were prosperous enough to do this properly did indeed do so, with full dining cars (with ever-better fare) and innovative moves to get more passengers on the routes making it easier and easier to operate the trains. The New York Central's 20th Century Limited and New England States, Pennsylvania's Broadway Limited and National Limited (the latter bought from the Baltimore and Ohio as they bailed out of the passenger business) and the Chesapeake and Ohio's Washington-Detroit Chessie ruled the Northeast, while the Super Chief, Golden State and City of Los Angeles slugged it out over the Chicago-Los Angeles route, the California Zephyr and City of San Francisco fought for the Chicago-San Francisco market and the Empire Builder and North Coast Limited fought to Chicago-Seattle, with the by then hugely-busy Coast Daylight linking the West Coast. Santa Fe's Lone Star soon also ran between Chicago and San Antonio, and the El Capitan became the night train complement to the Super Chief. The Southern's Southern Crescent and the Seaboard Air Line's Silver Star and Silver Meteor owned the Northeast Corridor to the South markets, with the Southern Crescent going to Atlanta, Birmingham and New Orleans while the Silver Star and Silver Meteor raced on to Florida. All by the late 1950s had given up on trying to compete with airlines on speed and instead fancied themselves as luxury hotels on rails, and it showed in ever-better amenities and ever-bigger consists. However, these tactics for the most part worked, and by the early 1960s, airlines that couldn't easily get into domestic markets (Pan Am in particular) were teaming up with the passenger trains to act as feeders into the airline network, using connections between the cities and airports that both sides (and the cities they served) were eager to build. Furthermore, reductions in freight traffic on the Northeast Corridor for the Pennsylvania opened up new possibilities, and the completion of a tunnel under Manhattan between the Pennsylvania and Grand Central Stations in 1962 opened up possibilities for through trains between as far apart as Boston and Washington, and the Pennsylania's trains of the corridor were incredibly busy, showing that if the speed and frequency were there, the possibility of wide-scale passenger traffic was there. Night passenger trains by the early 1960s were adding to this, as the New York Central's Watchman, which began operations in 1958, was a sign of what was to come - a night train with a first-class restaurant on board, it was meant for business travelers to get on after dinner in New York, sleep most of the way to Chicago, and eat a very good breakfast on the train before the train arrived in Chicago, and as if to make the point, the Watchman's sleeping cars came with showers and a robe service, so that riders could feel good and refreshed when they got off the train at either end of the route.
The authorization of the Shinkansen's construction in 1959 did not go unnoticed in America, and the New York Central, Santa Fe, Southern Pacific and Southern Railway all helped pay for part of the financial cost of the building of the Tokaido Shinkansen in return for understanding how the route worked. They, like many others, were more than a little surprised with the results of the Shinkansen, and the New York Central began planning a route built to similar standard before the Shinkansen went into service in October 1964. Such was the success of the Shinkansen that, despite the huge costs involved, the NYC and SP announced the building of their own high-speed lines, the NYC going from New York City to Albany and Buffalo as well as partnering with the New Haven to go New York to Boston in May 1965 and SP announcing its routes from Los Angeles to San Diego, Las Vegas and the San Joaquin Valley in June 1965. This led to the High Speed Ground Transportation Act of 1965, which both helped to fund and develop American high-speed trains and their infrastructure and to push for regulatory improvements. Pan Am also bought in, offering to assist the NYC and SP with the high-speed lines. The Pennsylvania Railroad was quick to jump on board, and in November 1965 work began to unify the entire Boston-Washington route in terms of signalling, power systems and loading gauge. This was finished rapidly, and the Metroliner and Empire State services began in May 1969, while the SP's San Diego Daylight began operations in June 1969. Aware of the benefits, the Pennsylvania's Keystone Service began operations from Atlantic City to Harrisburg via Philadelphia in April 1970 and, after extensive work in the San Fernando and Tehachapi Pass routes was completed, the San Joaquin Daylight and Las Vegas Daylight began operations in November 1971, this delayed by the San Fernando Earthquake in February, which had caused extensive damage to the newly-built line in Soledad Canyon.
The effect was hard to understate. New York City's problems in the 1970s led to an economic boom in upstate New York (particularly Troy and Albany), as people chose to live further away from the crime and poverty stricken big city while still having access to it. The Metroliner services were so popular by the mid-1970s that it actually caused a reduction in air traffic in the Northeast Corridor, and Atlantic City saw a major revival of its fortunes in the 1970s as travelers could reach it more easily. It was a similar situation in California, and perhaps more importantly the lines themselves proved to be hugely profitable for the Southern Pacific, New York Central and Pennsylvania. The Pennsy's 1973 bankruptcy and the formation of Conrail put the Northeast Corridor under the control of the Consolidated Rail Corporation, which promptly spun it off into Amtrak, which was formed in 1977 to co-ordinate the passenger rail services both public and private in the United States. Such was the success of the high-speed lines that others soon scrambled to jump on board, including the NYC itself, which began high-speed operations on its busy Chicago-Detroit Wolverine route in time for the American Bicentennial in 1976. Amtrak from its formation was meant to co-ordinate private-sector operations as well as take over those of railroads that sought to exist the passenger business. The bill that created Amtrak also provided funds and organization for cities to take over money-losing commuter operations, which proved a hugely-beneficial provision for railroads and created multiple agencies, including Metra in Chicago, Metrolink in Los Angeles, New Jersey Transit in New Jersey, Caltrain in the San Francisco Bay Area and SEPTA in Philadelphia, to handle the commuter operations. By the 1980s, cities both large and small that had troubles with traffic congestion were looking at commuter rail as a way of alleviating congestion.
One of Amtrak's long-term plans from its creation was to establish high-speed rail in the Midwest, but with the New York Central (on the Chicago-Detroit and Chicago-Indianapolis routes), Santa Fe (on the Chicago-St. Louis-Kansas City route) and Burlington Northern (on a Chicago-Milwaukee-Madison route) already working on that, Amtrak soon was working on filling in gaps, planning out high-speed service from Indianapolis to Cincinatti, Columbus and Louisville, Chicago to Cedar Rapids, Madison to the Twin Cities and Detroit to Toledo and Cleveland. On the latter route, the NYC beat Amtrak to the punch, their profitable lines in New York and Michigan leading to them having the confidence to plan an entire Chicago-New York high speed route, which they planned on opening in 1986. Conrail bought the Richmond, Fredericksburg and Potomac in 1980 specifically to use its main line from Washington to Richmond as a high-speed conduit, and they built from Washington to Newport News and Norfolk, opening the line in 1984. SP's high-speed lines extended from Bakersfield to Sacramento in stages between 1976 and 1980, and the company built across Altamont Pass to San Diego, Oakland and San Francisco, connecting San Francisco to the California High-Speed Rail Network in 1985.
As the high-speed routes got built, the freight railroads' confidence in their long-distance trains grew, and the development of Amtrak's Superliners in the early 1980s (themselves clearly inspired by the Hi-Level Coaches built for Santa Fe's El Capitan in the 1960s) was an impetus for railroads to both use the Superliners and develop their own double-deck car designs. Southern Pacific's 'California Cars' and 'Cuisine Cars' were one such result, the latter being rapidly copied by the Santa Fe for its high-end Super Chief. Amtrak, pushed by politicians, began to co-ordinate the trains of the New York Central, Conrail, Southern Pacific, Santa Fe, Burlington Northern, Chessie System, Southern, Seaboard Coast Line, Illinois Central, Rio Grande and Union Pacific with their own trains, serving the lower-demand areas with traffic to the privately-held routes, though Amtrak scored some big winners on their own, scoring with its Gulf Coast (Jacksonville-New Orleans), Music City Star (Charlotte-Asheville-Nashville-Louisville), Keystone Limited (Atlantic City-Philadelphia-Pittsburgh-Columbus-Detroit), Pioneer (Phoenix-Las Vegas-Salt Lake City-Boise-Portland-Seattle), South Wind (Chicago-Indianapolis-Cincinatti-Chattanooga-Atlanta-Orlando-Tampa) and International Limited (Chicago-Detroit-Toronto-Montreal). The willingness to have Amtrak's trains feed into the other named trains was very much appreciated by the other railroads, and so Amtrak's desired schedule shifts to accomodate connections were by and large accepted by the freight railroads, who noticed in the 1980s a sizable growth in ridership. Both the desire to have good train travel (helped by the growing high-speed network) and the luxurious trains themselves (by the 1980s, all of the named trains ran with three-unit dining car sets that served meals as good as most restaurants, along with lounge cars with leather seats and audio-on-demand systems with headphones, all trains used all bedrooms as roomettes disappeared in the 1970s) made sure the number of riders on the trains grew dramatically. By 1990, routes like the Super Chief, Empire Builder, California Zephyr and 20th Century Limited were routinely operating in multiple sections and the night train services were highly-popular on eastern routes.