President Obama expressed confidence Sunday that the Senate will "take the baton" and approve sweeping health care reform legislation, after the House narrowly passed its version Saturday night.

The president, in brief remarks from the Rose Garden in Washington, said the 220-215 House vote brings the country closer than it's ever been to a health care overhaul. Obama said the "historic" passage marked a "courageous vote" for many representatives, given the toxicity of the debate surrounding the bill, and predicted that lawmakers will view the eventual signing of the legislation as their "finest moment" in public service.

"Now it falls on the United States Senate to take the baton and bring this effort to the finish line on behalf of the American people," Obama said. "And I'm absolutely confident that they will."

But key senators suggested such optimism could be premature, with Republicans enjoying stronger numbers in the Senate and important differences between the House and Senate legislation still unresolved.

"The House bill is dead on arrival in the Senate," Sen. Lindsey Graham, R-S.C., said on CBS' "Face the Nation," noting that 39 Democrats "bailed out" on the bill Saturday night. "It was a bill written by liberals for liberals. ... So the House bill is a non-starter in the Senate."

More On This...

The Senate is not considering the House bill at the moment. The chamber has its own version of the legislation, which includes a different version of a government-backed health insurance plan, or "public option," and different funding mechanisms. But the differences between the two bills would have to be reconciled should the Senate approve its proposal.

Plus there are lingering bipartisan concerns in the Senate about the version Senate Majority Leader Harry Reid introduced weeks ago, raising questions about how quickly the bill can be brought to the floor.

Independent Democratic Sen. Joe Lieberman told "Fox News Sunday" that Democrats can certainly count him in the "no" column if they keep in a government-backed insurance plan.

"If the public option is in there as a matter of conscience, I will not allow this bill to come to a final vote," the Connecticut senator said, signaling as he has before that he would back a Republican filibuster -- which Democrats need 60 votes to break.

Reid had also lost the support of Maine Sen. Olympia Snowe, the only Senate Republican to have supported any version of Democrats' health care reform, after introducing a bill including a government option that allows states to opt out.

Most Democrats, however, were triumphant after Saturday's historic vote.

Sen. Jack Reed, D-R.I., said on "Face the Nation" that passing the bill out of both chambers is "essential," though he acknowledged there is a long road ahead.

"I believe we're going to pass health care reform. I believe we must do this because it's essential to not just the quality of life, here, but our economic success in the future," Reed said. "Harry Reid has introduced a public option. There's strong support there. But we are far from the end of the debate in the Senate. It will take time. It will be careful, thorough and deliberate."