I reckon that enough Canadians will be... if not happy with the US, then not willing to try a third rebellion, because they really don't want to risk having Saktasoon superbombed. So, while the occupation might last twenty or so more years, (probably with more than a little help from the Republic of Quebec) the generation born post GWII will think of themselves as Americans first and Canadians second-- this obviously discounts the large number of American citizens who move up to Canada of their own free will. So, by the 1960s, I reckon the Canadian provinces will be admitted to the Union. Off the top of the head, this'll probably save the US close to a million soldiers.
As for the CSA, well, that's where the problems arise. I get the feeling that the USA really views the Confederates as different to them by 1944. And if the occupations of Houston and Kentucky interwar were anything to go by, the USA will have a guerilla war on its hands stretching from the Gulf of California to the Atlantic Ocean. The average American views the Southerners as the eternal enemy of their country. Thus, the South will be an awful backwater and a really shoddy place to live. Obviously, as Ohio, Pittsburgh, and Philadelphia are reconstructed, the South will come dead-last in receiving aid (and it wouldn't surprise me a bit if the US government conscripts Southern civilians into labour units to rebuild the North). All this to say, the South will be a mess for a long time, and its people will still hate the Yankees in 1970 just like they did in 1870. Sadly, I don't think the Destruction survivors will be treated very well by the US government- the prevailing view seemed to be they're only... The US government will be too cash-strapped to provide the survivors payment, although granting them a ticket north and the vote might happen (the US would want people settling in Canada, Utah, and even devastated Ohio).
But the thing is, I imagine the North will sit on them forever if need be. TL-191 USA has seen two Great Wars on its home soil, the Midwest destroyed, and its capital nuked. The whole argument that "US society can't stomach high casualties" has been proven false. Ever since the Second Mexican War, the Remembrance ideology has made people venerate the military and think that "it's sweet and honourable to die for one's country". If Private John Smith from Flyover, Dakota gets blown up in the South by a Featherston Fizz in let's say, 1964, those who knew him will say "he did his duty, just like... (insert name of relative killed in GWII here)." Those Americans who advocate pulling out of the ex-CSA will be despised by much of the population-- as a matter of fact, now that I think about it, this could be an interesting bit of Turtledovian parallelism, young college students protesting to get out of the South. Who knows- that might develop into a counterculture analogue all its own.
As for the Republic of Texas, I don't see it lasting. President Dewey will inevitably see it as a "last bastion of Confederate nationalism", and worry that it'll set a bad precedent that the US is weak, and a "Republic of Carolina", or whatever, can be established with enough car bombs. If the Texan government doesn't vote to join the Union as a state by the end of 1945, Irving Morrel and Abner Dowling are going to get a fun new barrel park to test their latest machines in. What would make more sense- and be in keeping with Turtledove's parallelism- would be for Cuba to be given independence. It's not geographically contiguous to the rest of the US, and it's not seen as "Confederate"; ie, it's a different ethnicity to the Southern mainland, your average Confederate in the street wouldn't want to move there and probably wouldn't think of it much, but it'd be a safe place for those who really can't stand US occupation. If it's a choice between letting Cuba go or dealing with more people bombs, I know what I'd choose.
Sonora, Chihuahua, and Baja California (I think the US conquered it in The Grapple- no?) can be integrated pretty quickly, probably by the mid-to-late 50s.
As for the Mormons, well, this is where the US is really going to take the gloves off. Like the Canadians, there aren't many Mormons to begin with, but unlike the Canadians, the US hates them, views them as treasonous, backstabbing, polygamists who want nothing more than to set off a car bomb in the middle of a Remembrance Day parade. The US tried to give the Mormons statehood under Al Smith; look what that gave them. Thus, it wouldn't surprise me a bit if they went "full Featherston" here, and ethnically cleansed the Mormons.* Dumping them on the Sandwich Islands only invites them to rise up and look to Japan. The US public won't shed a tear.
Japan will most likely blunder its way into a war with the US before too long, and unlike in the '30s, the US will do a proper job. Either an IJN vessel and a USN one have an... unfortunate incident, or Japan does something equally provocative. My money is that it'll happen before 1980. TL-191 Japan has everything it could ask for, and TTL's leaders in Tokyo probably think they can do anything. When Japan and the US do go to war, Japan'll get curbstomped like OTL, but it will be bloody. Unless the war breaks out very early, think before 1950, both sides will have superbombs and won't be afraid to use them. If the war takes place in the 1960s, both sides will have enough ICBMs for this thing to go in a horrible direction. Think Japan getting blasted back to the Stone Age, but the West Coast of the US being obliterated. But assuming total nuclear holocaust is avoided, the US will win. Japan will no doubt foster an uprising in the CSA, which will tie one hand behind the American's back. But although TTL's Japan will be stronger than OTL's in the Pacific War, it'll still win eventually. Personally, I'd like to imagine Sam Carsten's exec Pat Cooley would be an admiral or something in the conflict, and perhaps Dowling's adjutant will be a general. America will try to establish puppets in the former Japanese Empire, but without much luck, as it'll be too busy close to home. Nuclear bombing will make an occupation of the Home Islands unnecessary.
Things like the space race and an alt-Great Society will be seriously delayed or butterflied altogether by the expenses facing the US. Personally, I doubt a serious Cold War with Germany will erupt- even if the two are competitors and dislike one another, there's an ocean separating their power blocs (whereas the US had ground troops and allies right next to the Warsaw Pact IOTL.) There won't be enough African-Americans left for a Civil Rights Movement to matter much any which way (although I expect President Dewey would enforce desegregation very early on, to present an unmistakeable message that times were changing).
All this will mean a tight squeeze on the US population. Universal conscription will last until the present day, most likely, with taxes much higher. Economics isn't my strong suit, but I'm sure the GDP per capita numbers will be much lower ITTL. If a martial culture persists for long enough, and especially if there's some sort of nuclear exchange with Japan, we could see a coup in the US, but frankly I doubt it.
Ultimately, I see TL-191 USA bearing the heavy load of holding its empire together at whatever cost.
*Obviously not condoning atrocities/ethnic cleansing/war crimes of any kind.
