WASHINGTON — President Obama on Tuesday affirmed his support for the creation of a government-sponsored health insurance plan, but he acknowledged that such a plan would sharply reduce the chances for Republican support of legislation to overhaul the health care system, Democratic senators said.

The senators, who met with Mr. Obama at the White House, said he also set forth a timeline, calling on Congress to send him a comprehensive health care bill by October.

“He wants the bill through the Senate and the House before the August recess, so we can conference and have it done in September and signed in October,” said Senator Barbara A. Mikulski, Democrat of Maryland. “He said we need to be unflinching and unflagging.”

In remarks just before the meeting, Mr. Obama said: “This is going to be a heavy lift. I think everybody understands that. But I’m also confident that people want to get this done this year.”

The Senate Democratic leader, Harry Reid of Nevada, said he believed that the full Senate should be able to take up the health care bill and “hopefully finish it” next month.

“But, you know, I don’t know,” Mr. Reid added. “We’ll have to see how long things take.”

In response to a question from Senator Jeff Bingaman, Democrat of New Mexico, Mr. Obama said that it was important to include a public plan option and that such a plan could help control health costs.

Senator Sheldon Whitehouse of Rhode Island, one of two dozen Democratic senators who met with Mr. Obama, said the president “spoke very enthusiastically about a public plan” that would compete directly with private insurers. The president’s words were comforting to Democrats like Senator Sherrod Brown of Ohio.

“The sentiment in the room, with the president and the rest of us, was that a public plan option will keep the insurance industry honest, will give people more choices in their health care and can save significant amounts of money,” Mr. Brown said.

But other senators at the meeting reported that Mr. Obama also said he wanted a bipartisan health care bill, and they said he recognized that Republicans were strenuously opposed to a government-sponsored plan.

Reid H. Cherlin, a White House spokesman, declined to characterize the president’s comments.

Other Democrats said Mr. Obama suggested that as “a show of good faith,” Democrats might work with Republicans on other issues, like medical malpractice. Many Republicans would like to limit the amount or types of damages available to patients who sue doctors, hospitals and other health care providers.

Another topic at the White House meeting was how to pay for covering millions of the uninsured.

Senator Max Baucus, Democrat of Montana and chairman of the Finance Committee, said Mr. Obama indicated that he “might consider” the idea of taxing some employer-provided health benefits, a proposal favored by Mr. Baucus.

“It’s on the table,” Mr. Baucus said. “It’s an option.”

The White House pushed back, saying Mr. Obama “made it very clear” that he preferred his own revenue proposals. Mr. Obama campaigned against taxing health benefits last year. Labor unions and many employers adamantly oppose a limit on tax-free health benefits.

But in a report on Tuesday, the Center on Budget and Policy Priorities, a liberal-leaning research and advocacy group, said, “Congress is unlikely to be able to finance health reform legislation that includes universal coverage unless it limits the exclusion of employers’ health insurance payments from workers’ income and payroll taxes.”

Senator Edward M. Kennedy, Democrat of Massachusetts, who is battling brain cancer, did not attend the White House meeting and is not expected on Capitol Hill this week. But the Committee on Health, Education, Labor and Pensions, of which he is chairman, met for more than an hour Tuesday to sift through options.

To help control costs, the administration indicated support on Tuesday for a proposal to strengthen a federal panel that recommends how much Medicare should pay doctors, hospitals, nursing homes and other health care providers.

Senator John D. Rockefeller IV, Democrat of West Virginia, recently introduced a bill that would expand the role of the panel, the Medicare Payment Advisory Commission, and give its recommendations the force of law. Senators said Mr. Obama and his aides had expressed general support for such a change, which would establish the panel as an independent rate-setting body in the executive branch.

Several senators said Mr. Obama had conveyed a sense of urgency and spoken emphatically about the importance of revamping the health care system in a way that would reduce costs.

“The president made clear that history will judge us by whether this bill controls health costs,” said Senator Ron Wyden, Democrat of Oregon.