Upon thinking a little more, I think I should just reemphasize--the decision to demobilize was clearly not a partisan whim of Truman's. Consider the parallel situation of Britain; the Tories under Churchill could have held off dissolving the War Cabinet and postponing elections until total victory, over Japan as well as Germany, was won, but their political calculation was that their best chance was an early election, to give Labour the least time to organize; Churchill and the rest of his party were confident they were going to win based on the wartime mentality. And yet Labour trounced them, and it was the Services vote overseas, permitting British subjects deployed all over the world to vote, that tipped the balance decisively. (Americans deployed overseas did not get to vote in 1944). After the election of 1946, Truman faced Republican majorities in Congress, and they too did little to check the tide of demobilization. Bear in mind the Cold War mentality was not really established until the Korean War. Prior to that, it was the Democrats who were more consistently in favor of military buildup and deployment, specifically against the Axis. I named Taft as an example of a Republican most extremely against the New Deal establishment, but I suspect his isolationist and fiscal conservative backers would be just as parsimonious about conventional military spending, if for very different reasons, as any New Dealer keen on turning guns to butter. The coalition equating a big military and conservative patriotism had simply not been formed yet; it had its exponents and backers, but nowhere near a national consensus yet.
It would then take some serious ATL spadework to prepare the ground in advance, before 1945's victories, for sustaining a big part of the mobilized force indefinitely after the war. The only plausible foe to maintain a big standing army against would be the Soviet Union, and there are those who argue that the Red Goliath of 1945 was made of clay, the Soviets so stretched thin by the rigors of the later part of the war that they were liable to collapse. I'm very skeptical of that, and would say rather that by remaining in occupation of Eastern Europe rather than returning to their decimated home, the Red Army maintained itself, eating up Soviet reparations on the spot as it were. If one assumes they would fight as tenaciously after victory as they did before then yes, the Red Army was a mighty steamroller indeed and keeping conventional forces in Western Europe that could check it conventionally would have been tantamount to keeping the lion's share of maximum WWII mobilization going. I do think the USA could have afforded to do it, economically. I don't think there would be anything close to a majority supporting it politically. Figures like Patton and MacArthur were out of step both with the New Deal majority on the left and with key bastions of right-wing support as well; the latter might applaud the destruction of the Red Menace, but not the tremendous distortion of US policy that would be involved in maintaining the standing army necessary to do it.
I suppose the least implausible means whereby the USA might have checked demobilization and maintained say a third or even half of the wartime peak might be if policymakers were to commit to defending Chiang Kai-shek's regime in China. It was self-evident in 1945 that to really commit, with no exit strategy other than victory, to that would surely mean sending a lot of GIs and associated kit to China and stationing them there, to immediately confront and most likely start shooting it out with Chinese Communists counted as allies during the war only yesterday. The US public had a huge dread of being bogged down in a land war in Asia, including vast legions who later never tired of baiting the Democrats with "Who lost China?" It would be politically ASB for any plausible US leader to openly and clear-sightedly commit to propping up the KMT come what may, but just perhaps, if Roosevelt had chosen a different running mate in '44 or one can finagle a Republican victory in 1940, just maybe a commitment that was hoped to be modest, just to stiffen up the KMT a little bit and take a firm stand against the ChiComs, might spiral, step by nightmarish step, into a full-blown US stand in China, which would turn into a nightmare to make Korea look like Candyland. That would perforce end the draw-down, but note only by sucking the USA into another war quite as nasty as any theater of the previous war. Almost certainly before it got to that level, we'd have generals using A-bombs to try to level the field a bit. What the Soviets would do, I'm not exactly sure!
What I am sure of is that any sensible US leader in the mid-40s would be very careful not to get drawn into that quicksand in the first place, and if it means Chiang must fall, so be it. Few would want to just wash their hands of him openly and cold-bloodedly, but many would seize on any excuse they could to avoid tying the fate of the USA to him irrevocably either. Mostly they'd kid themselves into thinking that with modest degrees of US aid Chiang could beat the Communists on his own, as they evidently did OTL.
Another aspect of going with adjusting things considerably uptime of 1945 by putting in a Republican in '40 might be that possibly an ATL Administration might not do the Manhattan Project at all, or take half-measures. Given that it delivered useful bombs, and then in literal handfuls, only by late 1945 OTL, any delays or soft-pedaling seems likely to mean no bombs available to the end of the of the war. This might mean that as the war approaches endgame, American policymakers have only the alternatives of either downsizing the US conventional forces and abandoning Europe and East Asia to Soviet influence, or somehow finagling US domestic support for sustaining the huge mobilization indefinitely. As I said this was hardly conventional Republicanism of the interwar years, so this is a tough row to hoe for any ATL.