WASHINGTON (Reuters) - Americans strongly support fundamental changes to the healthcare system and a move to create a government-run insurance plan to compete with private insurers, according to a New York Times/CBS News poll published on Saturday.

The poll came amid mounting opposition to plans by the Obama administration and its allies in the Democratic-controlled Congress to push through the most sweeping restructuring of the U.S. healthcare system since the end of World War Two.

Republicans and some centrist Democrats oppose increasing the government’s role in healthcare -- it already runs the Medicare and Medicaid systems for the elderly and indigent -- fearing it would require vast public funds and reduce the quality of care.

But the Times/CBS poll found 85 percent of respondents wanted major healthcare reforms and most would be willing to pay higher taxes to ensure everyone had health insurance. An estimated 46 million Americans currently have no coverage.

Seventy-two percent of those questioned said they backed a government-administered insurance plan similar to Medicare for those under 65 that would compete for customers with the private sector. Twenty percent said they were opposed.

President Barack Obama and many Democrats in Congress have argued a publicly run healthcare insurance plan would increase competition and drive down the high cost of care at a time when the U.S. economy is mired in a deep recession.

Republicans argue a public plan would drive insurers out of business and lead to a government-run healthcare system.

Democrats in the U.S. House of Representatives suggested this week that all Americans should be able to get insurance regardless of medical history and that coverage should be mandatory for individuals and businesses.

The proposal, contained in the latest House draft of the healthcare bill, would create new insurance exchanges where people shop around for health coverage. Whether a government-run plan has a role in such an exchange has spurred serious political debate.

Republicans, the minority party in Congress, have proposed more modest healthcare changes, but lack the votes in the House or Senate to push them through or derail the Democrats’ health reform drive. They have warned about the expected high cost of restructuring the healthcare system, projected at more than $1.5 trillion -- a huge expense for a nation carrying record budget deficits.

The Republicans also hope to gain traction by playing on fears a vast expansion of government could further hurt the economy and reduce the quality of medical care.

The poll found that people were uneasy about heightened government involvement in the healthcare sector, with 77 percent saying they were very or somewhat satisfied with the quality of their own care.

A total of 895 adults participated in the telephone survey, which was conducted from June 12 to 16 and had a margin of error of plus or minus 3 percentage points.