A majority of Americans say the federal government should guarantee health insurance to every American, especially children, and are willing to pay higher taxes to do it, according to the latest New York Times/CBS News Poll.

While the war in Iraq remains the overarching issue in the early stages of the 2008 campaign, access to affordable health care is at the top of the public’s domestic agenda, ranked as far more important than immigration, cutting taxes or promoting traditional values. Only 24 percent said they were satisfied with President Bush’s handling of the issue, despite his recent initiatives, and 62 percent said the Democrats — not the Republicans — were more likely to improve the health care system.

Americans showed a striking willingness in the poll to make tradeoffs for a better health care system, including paying as much as $500 more in taxes a year and forgoing future tax cuts. But the same divisions that doomed the last attempt at creating universal health insurance, under the Clinton administration, are still apparent. Americans remain divided, largely along party lines, over whether the government should require everyone to participate in a national health care plan, and over whether the government would do a better job than the private insurance industry in providing coverage.

Looking ahead to the presidential campaign, 36 percent of Americans said they had confidence in the ability of Senator Hillary Rodham Clinton, the New York Democrat, to “make the right decisions on health care,” while 49 percent said they were uneasy about it. But Mrs. Clinton, who presents herself as a sadder but wiser candidate on health care, retained the confidence of nearly 6 in 10 Democrats on the issue, despite the politically devastating collapse 13 years ago of the national health initiative she helped develop early in her husband’s presidency.