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.

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.

Republicans in Congress have fiercely criticized the proposal as an unneeded expansion of government that might evolve into a system of nationalized health coverage and lead to the rationing of care.

But in the poll, the proposal received broad bipartisan backing, with half of those who call themselves Republicans saying they would support a public plan, along with nearly three-fourths of independents and almost nine in 10 Democrats.

The poll, of 895 adults, has a margin of sampling error of plus or minus three percentage points.

Mr. Obama and many Democrats have argued that a public plan would be essential, in the president’s words, to “keep insurance companies honest.” But Mr. Obama has also signaled a willingness to compromise for Republican support, perhaps by establishing member-owned insurance cooperatives instead.

It is not clear how fully the public understands the complexities of the government plan proposal, and the poll results indicate that those who said they were following the debate were somewhat less supportive.

But they clearly indicate growing confidence in the government’s ability to manage health care. Half of those questioned said they thought government would be better at providing medical coverage than private insurers, up from 30 percent in polls conducted in 2007. Nearly 60 percent said Washington would have more success in holding down costs, up from 47 percent.

Sixty-four percent said they thought the federal government should guarantee coverage, a figure that has stayed steady all decade. Nearly 6 in 10 said they would be willing to pay higher taxes to make sure that all were insured, with 4 in 10 willing to pay as much as $500 more a year.

And a plurality, 48 percent, said they supported a requirement that all Americans have health insurance so long as public subsidies were offered to those who could not afford it. Thirty-eight percent said they were opposed.

In a follow-up interview, Matt Flurkey, 56, a public plan supporter from Plymouth, Minn., said he could accept that the quality of his care might diminish if coverage was universal. “Even though it might not be quite as good as what we get now,” he said, “I think the government should run health care. Far too many people are being denied now, and costs would be lower.”

While the survey results depict a nation desperate for change, it also reveals a deep wariness of the possible consequences. Half to two-thirds of respondents said they worried that if the government guaranteed health coverage, they would see declines in the quality of their own care and in their ability to choose doctors and get needed treatment.

“It is the responsibility of the government to guarantee insurance for all,” said Juanita Lomaz, a 65-year-old office worker from Bakersfield, Calif. “But my care will get worse because they’ll have to limit care in order to cover everyone.”

When asked their opinion of specific changes being considered in Washington, three-fourths of those surveyed said they favored requiring health insurers to cover anyone, regardless of pre-existing medical conditions. Only a fifth supported taxing employer-provided health benefits to help pay the cost of coverage for the uninsured. And there was deep uncertainty about whether employers should be required to either help insure their workers or pay into a fund for covering the uninsured.

Three of four people questioned said unnecessary medical tests and treatments had become a serious problem, suggesting that they would support calls by health researchers for a payment system that would better reward appropriate care. But an even higher number, 87 percent, said the inability of people to have the needed tests and treatments was a serious problem. One in four said that in the last 12 months they or someone in their household had cut back on medications because of the expense, and one in five said someone had skipped a recommended test or treatment.

The poll found that Americans were far less satisfied with the cost of health care than with the quality of it. Mr. Obama, who has emphasized the need to reduce costs, has found an audience for his argument that health care legislation is vital to economic recovery. Eighty-six percent of those polled said rising costs posed a serious economic threat.

Yet only a fifth of those with insurance said the cost of their own medical care posed a hardship. And only a fourth said that keeping health costs down was a more urgent need than providing coverage for the country’s nearly 50 million uninsured. That was a notable change from a Times/CBS poll taken in early April, when 40 percent said that controlling costs was more pressing.