This survey by Stanford University suggests the answer is yes:

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Notes: The surveys asked whether individuals agreed or disagreed with the statement “I would like to live in a society where government does nothing except provide national defense and police protection, so that people could be left alone to earn whatever they could.” This question wording is from Page, Bartels and Seawright (2013). Cell probabilities above give the percent that either somewhat or strongly agreed.

Based on the numbers for Democrats and Republicans, it looks like around 50% to 55% of Americans claim to support an extreme minimal state, which means Milton Friedman and Friedrich Hayek were more socialist that the typical American.

Or perhaps (as I’ve argued elsewhere) there is no such thing as “public opinion”. People are like electrons; you can’t measure them without changing their positions. Lots of people gravitate to the “wouldn’t it be nice” answers. As in, “wouldn’t if be nice to have a simple flat tax you could put on a postcard”. Or wouldn’t it be nice to have free health care for all. Or wouldn’t it be nice to spend more on education. Or have lower taxes. Or pay off the national debt. Or deport the “bad hombres”. Or have the government leave me alone.

Most people don’t have views that are internally consistent, so their “views” on public policy issues are strongly shaped by the wording of the polls. Next time a progressive tells you that “the polls show” that Americans agree with the Democrats, show them this survey.

Most politicians do not have a set of views that are entirely internally consistent, although they are a bit more so in places like the UK, where elections actually deliver governments with the power to enact legislative agendas. I recall reading that candidate Trump once confided to a friend that the best strategy was to just promise anything the public wanted to hear. Thus (unlike other politicians) he promised to pay off the entire national debt in 8 years. And he would do so not by raising taxes or cutting spending, but through “trade”.
Indeed he promised to slash almost everyone’s taxes while also boosting spending. That doesn’t sound too painful. Nor does building an expensive wall with Mexico’s money. Trump outflanked other politicians by not having even a tiny bit of lingering guilt about promising anything that sounded appealing. But when people criticize Trump for doing this, the average person just thinks, “all politicians do that”, which to some extent they do.

PS. The most accurate polls are where there is no “wouldn’t it be nice” position. Such as, “Who do you plan to vote for in next week’s election?” Those force the public to make a choice between two unpleasant alternatives.