So small government vs. big government is one of, if not the only, driving motivation of just about every political aspect of American Society (Does the government have a right to kill a prisoner? Does the Government have the right to allow slavery (there was a war over this issue) does the government have the right to punish hate speech? Does the government have the right to make a buisness do something?
There are a lot of terms for this aspect, but in legal parlemence it is the difference between "Enumerated and Unenumerated Rights/Powers" as described in the U.S. Constitution (Mostly the 9th and 10th amendment). The 9th Amendment is the Unenumerated Rights clause and says that rights of the citizens that are listed in the constitution are not the only rights listed, just the really really important ones. In fact, the United States Constitution doesn't actually list many freedoms of the citizens at all. Only Three (First, Second, and Third)... at the time of the authorship Bill of Rights' Authorship. Amendments 4-8 are considered "Justice Amendments" and are restrictions on the government in courts and legal matters, it pretty much encompassed every grievance they had against Britain during the Revolutionary War (Fun Fact... the Third Amendment was so egregious to the American citizens, that to this very day, no SCOTUS case ever hinged on the interpretation of the Third Amendment). The 9th Amendment was basically put in to tell the government that, just because the right isn't out right stated, doesn't mean it doesn't exist (the reigning philosophy is that the Constitution wasn't granting rights, but limiting the government from infringing on Natural Rights, which all humans have by dint of being human (God-Given Rights, but I'm trying to be secular about this). Tl;DR: We're lazy and only wrote three liberties and restriction on government on justice matters, but that doesn't mean there aren't more rights, so don't try to do it.
The 10th Amendment basically rebuked another possible argument by saying that, that the Federal Government does not have enumerated rights. It only has enumerated rights to do anything we said it could do in the Constitution and that if we didn't tell the Federal Government it can do something in the Constitution, it cannot do it. If there needs to be a governing body on a matter, it's a state government that can make calls not in the constitution... and if there isn't a need for a governing body, than it's an individual's choice.
Finally, noticing that this set up allowed states to decide if slavery was a thing and gave the Constitution had no rule on managing slavery, they basically passed the 13th Amendment (Saying that the Federal Government had the power to ban and enforce such a ban on slavery) and the 14th Amendment which basically says "If we explicitly said we don't want the Federal Government to have these powers, why the hell would we give them to you?!"
Limited Government is a bedrock of Liberal ideology (I'm using Liberalism in a much more broad form, rather than the term that Republican Voters call members of the Democrat Voters... but that's not a discussion for here. Just known that American Politics uses a lot political terms differently) and a Liberal Government is usually limited by a constitution that restricts the power and authorities of government to one degree or another (Australia's constitution exists in multiple governments and New Zealand and England don't have constitutions for almost every government that is a Representative Democracy, they all have constitutions, but they do recognize limits to the government).
In modern America, limited government is a major plank of the Libertarian party (another curious word use... It means different things on (almost opposite ideolgies even) depending on the side of the Atlantic you reside on. Favoring a smaller or limited government is specifically called Minarchism. A uniquely American school of thought is that of Jeffersonian Democracy, which basically holds that the power over an individuals life should be inversely proportional to the size of the government. So while an individual should have the most power over his or her self, followed by the local government, followed by the state, followed by the federal government (Power: Individual > Local > State > Federal) the scope of that power (How many individuals that power affects and how difficult it would be to reverse the decision or otherwise leave the scope) is lessened as you climb (Individual < Local < State < Federal).