A key Republican senator who President Obama hopes will support his effort to overhaul the nation’s health-care system urged him Sunday to take any plan for a new government-run program “off the table.”

Senator Olympia Snowe, a member of the Senate Finance Committee, where the most-watched version of the health care bill is being written, said on CBS’s “Face the Nation” that the so-called public option is “universally opposed by all Republicans in the Senate” and “therefore, there’s no way to pass a plan that includes the public option.”

Ms. Snowe, who has previously criticized the public option, said she thought it unwise at this juncture to be clinging to the public option because doing so “leaves open a legislative possibility that creates uncertainty in this process.” On the other, she said, scuttling the public option for good “could give real momentum to building a consensus on other issues.”

David Axelrod, one of the president’s senior advisers, signaled the administration was remaining flexible about the option.

“I’m not willing to accept that it’s not going to be in the final package,” he said on “Face the Nation” as the debate over health care again dominated the Sunday talk shows. However, Mr. Axelrod suggested that Mr. Obama would not insist on including a public option if that meant giving up a chance to transform the way the nation insures its citizens’ health.

“But what he also said and what we’ve all said is that this is not the whole of health insurance reform,” Mr. Axelrod said of the president. “And we should not let the whole debate devolve into this one question, circulate around this one question, and lose the best opportunity we’ve had in generations to do something very significant about a problem that just — that is just getting worse.”

In other television appearances, several Democratic lawmakers also played down the necessity of devising a government-run health plan as part of a health-care package. Sen. Dianne Feinstein, a California Democrat said on CNN’s “State of the Union” that there’s “more than one way to skin that cat” when it comes to lowering health care costs. And Sen. Jeanne Shaheen, a New Hampshire Democrat, said “I think that’s a reasonable way to go, but I think it’s important to stay focused on what we’re trying to accomplish.”

A new government insurance has been roundly opposedby the health care and insurance industries, and Republicans have argued that it would create an alternative to employer-sponsored private plans that will lure millions of insured workers away and lead to a dysfunctional single-payer plan.

Senator Mary L. Landrieu, the Democrat from Louisiana, joined that chorus on ABC’s “This Week with George Stephanopoulos,” arguing that a government-run health plan would “undermine the private insurance system that she said covered 55 percent of insured Americans.

“Let’s not revise the whole system, let’s build on its strengths,” she said.

Max Baucus, the Democratic chairman of the Senate Finance Committee, has said in recent interviews that he cannot get the committee to support a government-run health plan. Instead, he said, the committee is coalescing around a bill that would expand Medicaid coverage to several income brackets above the poverty level and require all American to be insured through private plans or through the existing public plans of Medicare and Medicaid. Subsidies would be provided for those who could not afford medical insurance.

One avenue for keeping the public option in any new health bill — even if delays its start — is a “trigger” mechanism that Senator Snowe has proposed and again she talked about Sunday. She said that if the nation’s 50 million uninsured are brought into a new health care system that relies largely on private insurance and that system does not work well, a public options could be automatically required some years down the line.

“Let’s give time for insurance reform to work, then we can have a trigger,” she said.

Senator Jay Rockefeller, a Democrat from West Virginia who supports a government-run health program, suggested on “This Week,” that the idea of nonprofit health cooperatives, an alternative being proposed as a means of introducing competition in states where health care is dominated by a single insurer, was a largely untested and marginal idea. He said there were fewer than 20 cooperatives in the entire country, with the only two that really work in Minnesota and Washington state.

Kathleen Sebelius, the Secretary of Health and Human Services, repeated assurances from the Obama administration that any new health plan would not include abortion as a reimbursable procedure, just as the Medicaid statute does not reimburse abortions now. On “This Week,” She pointed out that because of that assurance, the Roman Catholic bishops in America have decided to support an effort to overhaul health.

She also said that plan would not provide insurance coverage for immigrants who are here illegally.

“We do not believe that folks who are here illegally should have access to a new health insurance exchange,” she said, referring to the marketplace of sorts in which the uninsured would be able to select coverage through private insurance plans.

The talk shows included voiced skepticism that the Obama administration could bring down health costs without chiseling away at the care currently provided in Medicare and Medicaid, particularly for seniors. Senator Rockefeller said he would be willing to take on cost-cutting that “will be painful to a lot of folks, but not to seniors.”

Ms. Sebelius said waste can be cut out of current Medicare and Medicaid programs by lowering the cost the government pays for drugs and medical equipment for example and by cracking down on fraud.

When Gov. Tim Pawlenty, a Republican from Minnesota, said that government-run health plans have proved disastrous in the two states that tried them, Ms. Sebelius took exception.

“In Massachusetts, they readily admit that they expanded care and didn’t look at the cost side of the puzzle, which is why I think the president continues to suggest that anything we do, it has to bend the cost curve,” she said. “And as he said to Congress the other day, even if you bring down the rising health care costs .1 of a percent, you save $4 trillion over the first 10 years of the plan. So bending the cost curve has always been part of what Congress is talking about, and it’s impossible to do a state at a time. We need a national strategy.”