WASHINGTON - President Obama is making a mistake on health care by insisting on a government insurance option for the middle class, influential Republicans said in a letter to the White House released yesterday.

It could cost him a chance to have support across the political divide, the nine lawmakers, all members of the Senate Finance Committee, warned.

Leaders of the Finance Committee, which has the best odds of producing a bipartisan bill, are working against a self-imposed deadline for moving the legislation through committee this month. But tensions have risen since Obama recently affirmed his support for including the option of a public insurance plan.

"At a time when major government programs like Medicare and Medicaid are already on a path to fiscal insolvency, creating a brand new government program will not only worsen our long-term financial outlook but also negatively impact American families who enjoy the private coverage of their choice," said the letter, signed by all but one of the Finance Republicans.

"Democrats know that if they go to a totally partisan approach like the president has suggested they're going to eat that the rest of their lives," said Sen. Orrin G. Hatch (R., Utah), who circulated the letter to Obama.

"I'll be glad to help them, but not with a public plan," Hatch, referring to the Democrats, told Fox News.

Obama says his plan would allow Americans to keep private coverage. Many Republicans say that once a government insurance program is created, it will eventually dominate the market, and drive private insurers out of business.

Most Democrats support creating a public plan to compete with private insurers, but even they are divided on critical details. In the House, a rift has opened between conservative and liberal Democrats over a government plan.

The one Finance Republican who did not sign the letter was Sen. Olympia J. Snowe of Maine. Snowe has been trying to find a compromise under which a government plan would be available as a last resort, if health insurance remains unaffordable for many families even after Congress overhauls the system.

"If individuals are not offered affordable choices, the use of a fallback public plan as a last resort plays a critical role," Snowe said.

About two-thirds of Americans now have private insurance coverage, the vast majority through job-based plans. But there is one government health program that enjoys widespread political support.

Medicare, created for seniors more than 40 years ago, has defied the predictions of critics that it would usher in an era of socialized medicine. Though the government controls every aspect of the plan, Medicare recipients enjoy a wide choice of doctors and hospitals.

Some Democrats want to set up a Medicare-like plan that would, for the first time, offer government coverage to middle-class workers and their families.

Depending on how such a plan is designed, economists say it could force many private insurers out of business.

A government program would be able to undercut private insurers by paying doctors and hospitals less, thereby offering lower premiums that would draw employers and workers away from private insurers.

In the House, the 50 or so conservative Democrats who make up the Blue Dog coalition argue that the government plan must look and work a lot like private insurance, including being run by an outside contractor.