As many liberal policy wonks (not a pejorative) will point out: the American people love their welfare benefits! A common claim is that "A majority of Americans support $POLICY! It polls so well!", wherein $POLICY is broadly a sub-component of "welfare state". I sometimes hear it said with an undertone of exasperation: Why can't policies that are so self-evidently popular get enacted into law?

The challenge isn't getting people to say "Yes" when you ask them "Hey do you want all of this great stuff?" That already happens, per the above popularity of individual benefits.

The challenge is getting people to say "Yes" when you ask them "Hey do you want to pay for the government to give you all of this great stuff?" Those two details: higher taxes and government administration, are what erode support for these policies.

The median US citizen believes that "government run" is a synonym for any of dozen negative adjectives: wasteful, won't work, abused by the rich, bureaucratic, untrustworthy, and so on. Are those true or false in any given instance? Would a private sector alternative would avoid those negatives? The specifics do not matter when people are acting on deeply-entrenched, life-long perceptions.

As for why that perception came to be? That would be a historical thesis of its own, and might be tangential to your question.