I think the mentality comes from the perception (reality?) that we don't reap many benefits from the taxes we pay. The perception is that we pay taxes, and yet our public schools stink, we don't get free or cheap health care, we don't get lots of vacation time, we don't have limited work hours, we don't get high wages, we don't have great job security, etc. So, if you raise my taxes, how am I going to afford my (private) health insurance? And what benefit will there really be? I think that's how many Americans feel.
I think a big driving force behind this is that so many tax dollars vanish down the well of military spending and aid to prop up friendly regimes around the globe. A Norwegian pays taxes but she also sees the benefits of those taxes, she walks into a hospital and gets free health treatment. An American pays taxes and the money is drained into Iraq, Afghanistan, Israel, Egypt, Pakistan, developing a new super-duper full-spectrum stealth bomber, etc.
So American taxpayers react with the mentality of, okay, just don't raise my taxes and let me take care of myself.
OTOH if you look at something that has become accepted by historical precedent, like the public funding of fire departments, unemployment benefits, public schools and libraries, people are happy (in general) to pay taxes which often benefit others. The idea of "free books and education for all" has simply become accepted due to historical precedent, whereas "free health insurance for all" is a novel concept and many Americans believe it would be expensive.