Most people I've posed this question to tell me the United States started showing signs of becoming an imperialist empire around the turn of the twentieth century, when they began dabbling in smaller wars and tweaking international policy to .
However, I recently read through a couple essays (Richard Drinnon's The Metaphysics of Empire Building: American Imperialism in the Age of Jefferson and Monroe // Patrick Wolfe's Settler Colonialism and the Elimination of the Native) that suggest these ideas of empire actually started forming with the 1790 Naturalization Act, where citizenship was limited to white Americans, and the 1830 Indian Removal Act, where Native American settlements were moved further west to accomodate American farmers and settlers.
Do you think there is an argument for American Empire/Imperialism forming during the early 19th century, or not until after the Civil War?
Yes, I think so. There's been an odd imperial denialism in the United States, and this has extended into historical scholarship as well. Many historians didn't begin to name US imperialism until relatively recently, and when they did they began to engage in a bit of a game to pinpoint when exactly the US had its "imperial moment." Amy Kaplan was among the group of scholars in the 90s who saw 1898 as that moment, and she and others engaged in an extended re-evaluation of US empire -- focusing on categories of gender and culture, and on the reciprocal nature of imperial influence. That is to say, US empire didn't only have an impact abroad, it had an impact domestically as well. Other scholars, like Brian deLay or Shelly Streeby (I think), have pushed for 1848 as the true "imperial moment." Both 1898 and 1848 have the benefit (for purposes of definition) of a US military specifically reaching outside the boundaries of the US nation-state and engaging in wars intended to enlarge US territory.
My own orientation leads toward indigenous studies, and that means that I tend to take the position that the US has always been an imperial power. There's a naive question that's relevant here, which I like to use for teaching: if the early US wasn't an empire, how did it get so big? A common mistake -- and one that I think scholars who focus on the 1898 and 1848 moments make -- is to assume that a certain form European imperialism is the standard against which all other imperial endeavors must be judged. That has the bizarre effect (in my mind) of classifying British expansion into India as imperial (because the expansion wasn't contiguous with existing territory) and U.S. or Russian continental expansion as some other thing (because it WAS contiguous with existing territory).
The US did later engage in a foreign imperialism that was recognizably similar to European empires. But it also engaged in just the sort of settler colonialism that Patrick Wolfe describes -- not only in its early history, but during its own history as a colony. I don't have the numbers at hand, but it is instructive to look up just what an enormous percentage of US federal spending was taken up by the Indian wars in the first decades of US history. What to do with the naming of the US as imperial after we've gotten through that is another (more interesting) matter, of course.
If we define empire as being where one country essentially enslaves or conquers the population of another then I wouldn't say the Indians count, as we had no intentions of letting the Indians remain as opposed to just getting rid of them through murder or deportation. However the Mexican-American War and the acquisition of Texas probably counts, in my opinion. The war was at least partly provoked by upper class Southerners wishing to expand slavery into Mexico. At the same time it was a somewhat popular sentiment among the antebellum slaveowning aristocracy that the US should invade and annex most of Central America and in effect turn it into a gigantic slave plantation: See here
http://en.wikipedia.org/wiki/Knights_of_the_Golden_Circle
It's important to distinguish between movements that are superficially similar and not paint them with the same brush, though. I would say America in general did not do the same "kind" of imperialism that European countries did very much. Within the US there was a strong push to expand the territory of the US, but that involved simply killing, deporting, or assimilating any population that already lived there. The US never relied on colonies economically like European countries did. The closest the US got to European style imperialism was probably the Philippines, and even then the US didn't have an enormous interest in it.