Depends on which cohort of Americans you're talking about, but it's less that they see it as the government supporting them and more that they see it as the government "giving back what they owe." Social Security and Medicare have always been framed as something you pay into now and get back later in life, like you're lending money to the government. That's why most Americans don't view it as government support in the way Europeans do, and why they see no hypocrisy in spitting venom at "government handouts" while cashing their Social Security check and Medicare coverage.