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.