The long and short of it is that the Cold War shifts the opinion of conservative Americans.

Prior to WWII, the norm in American life as you note is a small standing army except in times of war; otherwise, what military is necessary is generally deemed to be a navy, not an army. WWII sees the creation of an uncommonly large American army, but in addition to that, the deployment of American troops to corners of the globe that aren't necessarily front-line areas. American troops are sent to Iran, for example, and American commitments are increasingly established with other countries that are essential to American security. For example, the United States forms closer ties with Saudi Arabia, not coincidentally because the pressures of the war change the United States from an oil exporter to an oil importer.

Ok, that's all well and good, but the war ends. There are plenty of U.S. conservatives like Robert Taft who want the U.S. army to shrink, and it does shrink dramatically in these years. Given that it goes from approximately 12,000,000 in 1945 to around 1,500,000 in 1950, and many American troops are tied down in occupations around the globe, one gets a sense of how quickly demobilization unfolds. Defense spending as a percentage of GDP is around 40% during WWII, down to 7.2% by 1948.

However, the Cold War begins to undermine this belief. Conservative Americans can really be united in their hatred of the Soviets (Jerome Himmelstein's To The Right argues that it was essential to forging a conservative coalition in the wake of the Cold War). By 1947, U.S. foreign policymakers largely embrace the notion of containment, which was to hold the Soviet Union in check and prevent its expansion until it either collapses or reforms. Its author, George Kennan, largely envisioned this policy as being based on military and economic aid to western nations; he was strikingly ambivalent about the CIA and didn't think that U.S. resources could support indefinite military interventions. Yet nevertheless, the military could be an important commitment to allies, especially given the resources of the USSR. Maintaining a stronger military would be important.

Taft, who could certainly lay claim to being the preeminent American conservative in the 1940s and early 1950s, never really finds a coherent way to oppose communism and the Soviet Union without some kind of support for intervention. He opposes NATO because it seems to tie down the United States, but not because he opposes U.S. intervention in the event of Soviet hostility. So, some kind of U.S. military is necessary to defend U.S. commitments and to preserve the U.S. position in the world.

One thing that both Democrats and Republicans are also consumed with is the idea of enabling long-term military spending without creating what they often term a "garrison state," which would undermine American civil liberties and weaken the American economy. Michael Hogan's A Cross of Iron focuses on this to considerable effect, noting that key compromises help to win people over. He argues that part of this were limitations on domestic spending to support the military, but also included were a prohibition on Universal Military Training, the National Security Act of 1947, and so on. These win over conservatives.

Lastly, there's the Korean War. Remember how much the U.S. military had shrunk, and how low spending had dipped? Once South Korea is invaded in 1950, the U.S. military is actually surprisingly hard-pressed for a bit because it's short of manpower and effective materiel. Concurrently, planners had been preparing a new policy that was to be called NSC-68 that called for, among other things, massive increases in the U.S. atomic arsenal, and, notably, conventional military forces. Korea didn't create NSC-68, but it helps to justify it in the eyes of Truman and, just as importantly, most of Congress. American defense spending shoots back up to 15% during the Korean War, and troop levels go up to around 3,500,000 as well. They dip again when the war ends, but they never go back down to their pre-Korea levels. In effect, some kind of permanent military establishment, and not just one built on nuclear weapons, remains to stay after Korea.

Hopefully, that was enlightening.

Jerome Himmelstein, To The Right

Michael Hogan, A Cross of Iron

George Nash, The Conservative Intellectual Movement Since 1945

James Sparrow, Warfare State (I know I just said a great deal about the Cold War being critical to this, but Sparrow points out how the war shaped American government too)