You surprised? Gee, me neither!

Americans overwhelmingly support substantial changes to the health care system and are strongly behind one of the most contentious proposals Congress is considering, a government-run insurance plan to compete with private insurers, according to the latest New York Times/CBS News poll.

The poll found that most Americans would be willing to pay higher taxes so everyone could have health insurance and that they said the government could do a better job of holding down health-care costs than the private sector.

Yet the survey also revealed considerable unease about the impact of heightened government involvement, on both the economy and the quality of the respondents’ own medical care. While 85 percent of respondents said the health care system needed to be fundamentally changed or completely rebuilt, 77 percent said they were very or somewhat satisfied with the quality of their own care.

Gee, New York Times, do you think the paradox might be that even if they like their insurance (and by that, they usually mean their doctor and the ease of use), they also know their insurance can be yanked if they ever get really sick?

That paradox was skillfully exploited by opponents of the last failed attempt at overhauling the health system, during former President Bill Clinton’s first term. Sixteen years later, it underscores the tricky task facing lawmakers and President Obama as they try to address the health system’s substantial problems without igniting fears that people could lose what they like.

Across a number of questions, the poll detected substantial support for a greater government role in health care, a position generally identified with the Democratic Party. When asked which party was more likely to improve health care, only 18 percent of respondents said the Republicans, compared with 57 percent who picked the Democrats. Even one of four Republicans said the Democrats would do better.

The national telephone survey, which was conducted from June 12 to 16, found that 72 percent of those questioned supported a government-administered insurance plan — something like Medicare for those under 65 — that would compete for customers with private insurers. Twenty percent said they were opposed.