A long and often riveting day did little to break the deadlock, reports our correspondent, and healthcare reform, which everyone wants, is no closer as a result.
The two sides clashed, mostly politely but sometimes angrily, over a host of technical and philosophical differences.
The White House has signalled it may end up driving through a bill using a procedure called budget reconciliation, which only needs a simple majority of 51 votes in the Senate.
Mr Obama said Americans wanted a final vote on healthcare. "I think that most Americans think a majority vote makes sense," he said.
Analysts say that was a hint he may drive the reform bill through Congress.
The reform plan is currently blocked as the Democrats no longer have the 60-seat majority required to thwart Republican obstruction tactics.
The contentious debate was plagued by partisanship: even the shape of the table for the debate at Blair House, opposite the White House, was the subject of dispute.
President Obama, Vice-President Joe Biden and other leading Democrats sparred with senior Republicans, including Mr McConnell and Arizona Senator John McCain.
Mr Obama urged the lawmakers present to avoid political theatre
Mr Obama opened the debate by emphasising that everyone present understood the importance of the healthcare issue, adding that there were significant points of potential agreement between the two parties on healthcare reform.
"We all know this is urgent and unfortunately, despite all the negotiations that have taken place, it became a very ideological battle; it became a very partisan battle where politics ended up trumping common sense," he said.
He added that he wanted to avoid the televised session becoming merely political theatre, hoping that those involved would work together to try to solve the problem.
"If we keep an open mind and are not trying to score political points then we may be able to make some progress," he said.
Republican Senator Lamar Alexander responded by saying that in order for Mr Obama to succeed on healthcare, he should scrap the health care bill that Senate Democrats passed in December, and start afresh with a clean sheet of paper.
"If we can start over, we can write a healthcare bill," he said. "It means working together... reducing healthcare costs... and going step-by-step to regain the trust of the American people."
Republican Senator Jon Kyl went on to argue that Democratic efforts to overhaul the current system would give Washington too much control over healthcare.
"There are some fundamental differences between us here that we cannot paper over," said Mr Kyl. "We do not agree about the fundamental question about who should be mostly in charge.
Cost of reforms?
The BBC's Mark Mardell in Washington says that while the president chaired the meeting firmly, trying to drag the Republicans into a concrete debate on detailed issues, there was almost no chance of the Republicans agreeing to anything that was on the table.
John McCain accuses President Obama of "unsavoury deal-making"
The House of Representatives and the Senate passed separate healthcare bills at the end of last year.
But efforts to merge them and sign a bill into law collapsed last month when Republicans won a special election in Massachusetts.
The victory deprived Democrats of their crucial filibuster-proof 60-seat Senate majority.
Republicans used Thursday's talks to highlight the cost of the Democrats' reforms, while outlining their own more scaled-back approach.
Democrats are expected to seek to portray the Republicans' plans as inadequate.
The president has invested much political capital in his plans to make nearly all Americans take out health insurance and to stop abuses by insurance firms.
But the issue has become a rallying standard for conservatives, who say Mr Obama is bent on introducing European-style big government.
It has also worried a recession-mauled American public, which is not clear about how much reforms would cost them.
The US is the world's richest nation and the only industrialised democracy that does not provide healthcare coverage to all its citizens.
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