Separately, some Congressional staff members expressed concern that Mr. Obama’s meeting would simply prolong an already tortuous process. And Democrats still face steep challenges in reconciling the differences between the House and Senate bills.

Some House Democrats are firmly opposed to a proposed tax on high-cost employer-sponsored insurance policies, which they think will hit some middle-class workers and violate Mr. Obama’s campaign promise not to raise taxes on Americans earning less than $250,000 a year.

The president offered a number of questions that his party would have for the Republicans.

“How do you guys want to lower costs? How do you guys intend to reform the insurance market so that people with pre-existing conditions, for example, can get health care?” he said. “How do you want to make sure that the 30 million people who don’t have health insurance can get it? What are your ideas specifically?”

The question for Mr. Obama is how much  if at all  he is willing to give on some of the concepts Democrats have already agreed on, or if he is using the meeting to lay the groundwork for another effort by Democrats to push the legislation through without Republican votes.

Mr. Obama did not indicate what he was willing to give up in the negotiations, nor did he chart a specific legislative strategy for moving a bill through Congress. Democrats in the House and Senate were hoping to resolve their differences in the bill, aides said, and present a unified health care plan in time for the meeting.

Senator Mitch McConnell of Kentucky, the Republican leader, said in a statement that he welcomed the bipartisan meeting on health care and called on the president to begin the dialogue “by shelving the current health spending bill.”

“The fact is Senate Republicans held hundreds of town halls and met with their constituents across the country last year on the need for health care reform, outlining ideas for the step-by-step approach that Americans have asked for,” Mr. McConnell said. “And we know there are a number of issues with bipartisan support that we can start with when the 2,700-page bill is put on the shelf.”