Isolationism
I think somebody brought up the possibility of an Isolationist United States as a possibility. While that might bring about the scenario in question, there are some reasons to think that that might not be the case.
The thing about Isolationism is that, in itself, it isnt necessarily anti-navy. It may shape the nature of a navy; for instance, ships with limited ranges, and an emphasis on defense (slow, heavily armored ships, coastal fortifications). But it is not, per se, against the presence of a strong navy, and in some cases actually favors one.
Let us take Britain as an example. An imperfect one, to be sure, because the english were never isolationists, but the overriding foreign policy goal of opposing continental hegemony is close enough for our purposes. Britain could have, if it so chose, recused itself from continental affairs and downgraded the navy to focus on an army to defend the shores and keep order, or built an army to contest control of the continent. But, from the Restoration on, the royal navy became more and more important, eventually becoming the senior service.
Why? Several reasons. A navy can be aggressive, but is in the British (and American) case firstly a bulwark against aggression. It is reliable; with a very few exceptions (Greece and occasional occurances in Latin America), navies as a rule do not become as involved in politics as the army. They do not threaten a constitutional government; using the british example, the navy never threatened to radicalize and overthrow the government, as the New Model Army defeated Charles (although there were mutinies), nor did it offer a route for the government to oppress.
Now, let us consider the Americans. One of the driving ideals behind American Isolationism has been the idea that the two oceans remove America from enemies, rivals, and conflict. With that in mind, a Navy is a deterrent, keeping other nations from casting a wandering eye upon American shores. It does not offer the same specter of interference in politics, for or against civilian government, that a standing army does. And, because it cannot strike inland, it appears less aggressive.
Finally, periods of isolationism in American history tended to coincide with interference in Latin America. For those purposes, one does not need a truly modern army, merely one with enough competence to handle the nation being intervened in. However, a navy is relativly crucial, both for logistical purposes and to deal with the local navies (the ABC powers, for instance, operated battleships). So, an isolationist government (albiet one involved in latin america) may actually have more need of a navy than of an army.