"44% of Americans think that prostitution should be legal while 46% think that it should be illegal. Democrats tend to support rather than oppose legalization (50% to 40%) while most Republicans oppose rather than support legalization (54% to 34%). Independents are evenly split, 45% to 45%."
As I expected, men are more pro legalization (59%) than women (30%).
I think you underestimate the left's anti prostitution fervor. Their stated arguments are around exploitation and trafficking.
I think polls usually undervalue how motivated people are to act politically on their stance. In the presidential race, this is related to how "energized" people are to go to the voting booth.
Either way, I think Americans have tended to outlaw borderline issues, but I suspect in the coming 1-2 decades, there will be a significant pushback against over-criminialization of non-violent crimes. There is a book called "Three Felonies a Day" which explains how ridiculous our laws have already become.
I doubt most people strongly want to outlaw adult, consenting prostitution. But the religious (socially conservative, etc) lobby is loud and participates when the law is challenged. The majority if people don't, so they tend to get what the anti-protitution lobby wants.