Speaking from the White House about 14 hours after the late Saturday vote, Mr. Obama urged senators to be like runners on a relay team and "take the baton and bring this effort to the finish line on behalf of the American people."
The problem is that the Senate won't run with it. The government health insurance plan included in the House bill is unacceptable to a few Democratic moderates who hold the balance of power in the Senate.
If a government plan is part of the deal, "as a matter of conscience, I will not allow this bill to come to a final vote," said Sen. Joe Lieberman, the independent whose vote Democrats need to overcome Republican maneuvers to kill the bill. He spoke on the Fox television network.
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"The House bill is dead on arrival in the Senate," Sen. Lindsey Graham, a Republican, dismissively told CBS' "Face the Nation" host Bob Schieffer.
Mr. Obama has made reforming the U.S. health care system a priority for his administration.
The United States is the only developed nation that does not have a comprehensive national health care plan for all its citizens.
The government provides coverage for the poor, elderly and military veterans, but most Americans rely on private insurance, usually provided through their employers.
With unemployment climbing, many Americans are losing their jobs - and their health insurance. Some employers don't offer insurance. As a result, there are nearly 50 million uninsured Americans.
Senate Majority Leader Harry Reid has yet to schedule floor debate and hinted last week that senators may not be able to finish health care this year.
CBS News correspondent Nancy Cordes reports rumors are circulating on Capitol Hill that Reid may even hold rare Saturday sessions in December for lawmakers to try and find a compromise suitable to all party members.
The House vote provided an important lesson in how to succeed with less-than-perfect party unity, and one that Senate Democrats may be able to adapt. House Democrats overcame their own divisions and broke an impasse that threatened the bill after liberals grudgingly accepted tougher, as abortion opponents demanded.
In Senate, the stumbling block is the idea of the government competing with private insurers. Liberals may have to swallow hard and accept a deal without a public plan to keep the legislation alive. As in the House, the compromise appears to be to the right of the political spectrum.
Republican Sen. Olympia Snowe, who voted for a version of the Senate bill in committee, has given the Democrats a possible way out. She's proposing to allow a government plan as a last resort, if after a few years premiums keep escalating and local health insurance markets remain in the grip of a few big companies. This is the "trigger" option.
That approach appeals to moderates such as Sen. Mary Landrieu, a Democrat. "If the private market fails to reform, there would be a fallback position," Landrieu said last week. "It should be triggered by choice and affordability, not by political whim."
Lieberman said he opposes the public plan because it could become a huge and costly entitlement program. "I believe the debt can break America and send us into a recession that's worse than the one we're fighting our way out of today," he said.
For now, Reid is trying to find the votes for a different approach: a government plan from which individual states could opt.
The Senate is not likely to jump ahead this week on health care. Reid will keep meeting with senators to see if he can work out a political formula that will give him not only the 60 votes needed to begin debate, but the 60 needed to shut off discussion and bring the bill to a final vote.
Toward the end of the week, the Congressional Budget Office may report back with a costs and coverage estimate on Reid's bill.
Reid has pledged to Mr. Obama that he will get the bill done by the end of the year and remains committed to doing that, according to a Senate leadership aide.
Both the House and Senate bills gradually would extend coverage to nearly all Americans by providing government subsidies to help pay premiums. The measures would bar insurers' practices such as charging more to those in poor health or denying them coverage altogether.
All Americans would be required to carry health insurance, either through an employer, a government plan or by purchasing it on their own.