Biggest butterfly to avoid here is Penn Central. That behemoth had no prayer of survival, the poor decisions by its management in 1968-70 were just the last in a very long string of mistakes made by the industry. The ICC was never going to allow a merger between the Pennsy or New York Central and a western railroad, and you'd need to consolidate to a considerable degree just to allow them to survive.
With a POD after 1946, you can make many butterflies. You could have the ICC neutered as the Staggers Act did, or you could have the railroads get new customers to sustain operations through various ways. The Pennsy was a pioneer in trailer on flatcar and container service (they called them Trail Van service, the name persisted through Conrail), so you could have that expand further. Hoist40's comment about union demands is also true, the days were ridiculously short and companies had to operate many lines that weren't profitable, but abandonment of most would need to be ICC approved and they were glacier-slow at that.
Saving some of the smaller lines is easy. Erie Lackawanna, for example, by 1970 was pretty much a line from New York to Chicago, with branches to Indianapolis and St. Louis that went into Conrail. Most of the former EL was abandoned, of course, though today part of it is the line Steamtown runs on out of Allentown, PA. The EL could focus on its long-distance runs from the NY area to Chicago and St. Louis, and if they did an agreement for traffic transfer to one of Western roads (The Santa Fe the most likely candidate), they could survive fairly easily.
Near-total consolidation is tough to get around. If you butterfly Penn Central, then the Pennsylvania is gonna have to complete with the EL and NYC across routes, and that would be a tall order. What might work there is for the New Haven to sink and Pennsylvania picks up some of its routes for a song, takes over the entire Northeast Corridor and focuses on moving loads, both of merchandise trains and of heavy commodities like coal. NYC could make it, but again, having both of them would mean Chessie has to be reduced to a minor player in the area and the EL has to barely stay afloat, any more than that and you saturate the market. The trucking industry and reduced industrial (particuarly coal and steel) traffic pretty much doomed Reading Lines, Lehigh Valley, Central of New Jersey and Boston and Maine - these will have to consolidate to some extent, no matter what, and most of the former CNJ and LV pretty much disappeared even under Conrail. When I wrote Transport America, I had President Eisenhower reward the railroads for their busting their arses in WWII by making sure they got considerable subsidies to go into improvements in their infrastructure - Penn Central was the poster child for letting this deteriorate to a terrifying level - and improvements to their operations. Even with that, with the advent of trucking systems and diesel locomotives, major financial difficulties for the railroads were inevitable.
With a 1946 POD, you could have the US choose to massively expand the coal-to-oil technology that they themselves had pioneered during WWII, which would be a major source of coal revenue for the railroads (you can't really move coal any other way).
Into the 1950s, Washington provides subsidies and money to improve the railroads' operations, which in the 1950s is mostly used to replace steam locomotives with diesel ones. The first trailer-on-flat car trains appear in the late 1950s. Falling passenger traffic is answered on several of the best passenger trains by continual service improvements and the marketing of the trains as a more comfortable way to get where you want to go rather than the faster airlines, a trend that is heavily added to after the advent of the Boeing 707 and Douglas DC-8 airliners in the late 1950s. As the last steam engines are cycled out of service in the late 1950s, rail car fleets begin to be rebuilt as well, with hundreds of thousands of cars built in the 1960s, and on main lines concrete ties, stainless steel rails, CTC and improved traffic management systems improve the speed and frequency of train operations.
The Virginian Railroad is bought by the N&W in 1959, the first of a long series of rail mergers. By now, New York Central, under Alfred Perlman, was jumping into the idea of railroads as an integrated transport business with both feet, and one of the NYC's good purchases was the purchase of the Schneider National trucking company in 1964. The company also sought mergers of its own, but ICC problems and the vast amounts of commuter traffic in the New York area hampered this. Regardless, the NYC saw a slow but steady rise in its traffic in the 1960s, and its deals with National, allowing for truck drivers to only have to take trucks to terminals, proved to be a highly successful enterprise. The NYC scored a big coup when they got approval in 1968 to build a tunnel under New York Harbor for its trains. The NYC also got help from an unlikely helper - Pan American World Airways, who starting in 1966 began helping the railroad improve its passenger service. While the NYC's high-end long-distance passenger trains, most notably the 20th Century Limited, New England States and the Motor City Challenger (the renamed Detroiter) all kept their fleet of passenger cars and equipment, the company, on the advice of Pan Am, began introducing the "Intercity Express" trains, using powerful CODAG propulsion systems to give the trains a top speed of over 125 mph, which began operating on shorter routes in 1968. These fast trains proved to be a major help to both domestically route-deficient Pan Am and to the passenger operations of the NYC.
By contrast, the Pennsylvania Railroad stuck to the idea that it was a railroad first and foremost, focusing more of its efforts on long distance heavy trains. Unlike the NYC and its extensive improvements to passenger operations, the PRR largely ignored that section of the business after about 1955, though it expanded its New York commuter operations in the 1960s. A boom in coal traffic helped with finances, but the PRR was starting to fail by the early 1970s, and the extensive damage done to their operations by Hurricane Agnes in 1972 put an end to their wishes to stay afloat. Losing several major freight contracts because of problems in shipping in 1967-71 added to their problems, and the PRR declared bankruptcy in September 1972, which caused the dominoes to crash. Reading Lines, Central of New Jersey, New Haven, Lehigh Valley and Boston and Maine followed within weeks. Erie Lackawanna and New York Central squeaked through, but the mighty Pennsy looked to be headed for collapse.
Into this fight came Perlman's "Green Team". Many of these people left the NYC for the Pennsylvania as the Pennsy was broke, and the new boss, former Santa Fe Chairman John Shedd Reed, came into the business in 1974. Reed proposed a huge, government-assisted program in which the Pennsylvania and its broke rivals would be consolidated into a major company, with stockholders in all the railroads being given stock in the new company, and the government's money being limited to loan guarantees, not grants. The message was simple - we need the money to survive now, but get us the resources we need and we'll fix this mess.
President Ford and the United States Congress figured this was the best way to save rail transport across a considerable portion of the railroad's territory, and agreed to plan, providing a massive $525 million in loan guarantees to the railroad, and proposing a substantial cut in the railroad's territory. The new firm would leave out big portions of the Readling Lines and Lehigh Valley, and nearly all of the Central Railroad of New Jersey. A second route along the Atlantic Coast would be assembled from the lines of the New Haven, allowing the Northeast Corridor north of Boston to be passenger and mail service only. It was a big and audacious plan, but it looked like it working would be likely, and the plan went into action in September 1975. The new Pennsylvania Railroad shed over half of its branch lines, but gained in its long-distance routes, and massively expanded their involvement in trucking business. The introduction of cheap, durable fiberglass skids to make ship in less than carload amounts added to the railroad's traffic, and expanded computer systems made that movement easier still. Many of the ideas were ripoffs of the work at the NYC, but as the 1970s went on, the Mighty Pennsy returned from the ashes, returning to profitability in 1979. Many of the lines not picked up the revitalized Pennsylvania were sold to smaller operators, who figured they could make them work themselves, while other lines wound up being rebuilt by several companies, including Canadian Pacific, Chessie System and Norfolk and Western, across the 1980s and into the 1990s.
Perlman had hardly retired from the New York Central in 1977 when he got the stunner of a lifetime. His protege and successor, Robert Flannery, announced in January 1980 that the NYC was in negotiations to buy out the Milwaukee Road, which had been economically failing for the best part of two decades. The real prize for this was the Milwaukee's Pacific Extension - a route which would fulfill the long-held dream of a transcontinental railroad which Perlman and his mentor, Robert Young, had dreamed of. The ICC, realizing that the Burlington Northern's dominance of the Northwest could not be broken any other way, approved the deal, and the company's stockholders approved that the NYC would purchase the Milwaukee, with the the Milwaukee's name being changed to the American Pacific Railway, and the two companies both using dark green and white paint schemes, with the NYC using mostly-green with white trim and lettering, and the American Pacific using the opposite paint.
Erie Lackawanna survived, wedged between the giants in the Pennsylvania and New York Central, but with the boom in heavy freight transport starting in the late 1970s, EL began effectively a feeder for the Western railroads, the Santa Fe in particular, while traffic moved both ways. The EL's survival was assured by its improvements in the 1970s, as they too went to heavy rail, concrete ties, heavy ballast and high-end signalling systems, allowing the EL's "express freight" trains to begin operating at speeds of 80 mph in 1981. The electrification built on the lines in the 1970s helped this.