"Obviously, they don't have the votes yet. I know they're working very hard," Cantor said. "The problem is I think there's a lot of uncertainty still surrounding this bill and frankly the American people, I think, think that there's a better way."
House Democratic leaders are pushing hard for a vote by Saturday, before Obama leaves for his international trip.
With time running out, Democratic leaders met until late into the night, gearing up for the final battle over health care.
On Tuesday, Speaker of the House Nancy Pelosi, D-Calif., told reporters she is waiting on numbers from the Congressional Budget Office analyzing the cost of Obama's health care bill, which proposes "fixes" to the Senate health care bill passed on Christmas Eve. But she reiterated that Democratic leaders will continue to fight for the health care bill despite objections from Republicans.
"We will do whatever is necessary to pass a health care bill," said Pelosi.
The opposition has stepped up the heat on lawmakers. On Tuesday, tea party protestors gathered once again on Capitol Hill to denounce the bill. Holding signs and chanting "Kill the Bill," the riled-up attendees took their protests into the halls of Congress, even though many lawmakers were not in their offices.
The congressional switchboard was overloaded for most of the day after conservative commentator Rush Limbaugh gave out two toll-free numbers for the public to call and urge their lawmakers to vote against the bill.
Republicans are accusing Democrats of dirty tricks.
"Last year, they [Democrats] thought they could pass a bill without having to read it. This year they want us to pass a bill without having to vote on it," Rep. Tom Price, R-Ga., charged at a rally Tuesday.
Obama continues to telephone skeptical lawmakers to urge them to vote for the bill. In an exclusive interview with ABC News on Monday, he expressed confidence there would be enough votes in the House to pass the health care legislation.
"I believe we are going to get the votes, we're going to make this happen," Obama said in an interview with ABC News' Jake Tapper.