"Obviously, they don't have the votes yet. I know they're working very hard," Cantor, R-Va., said on "GMA." "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."
The White House wants the House to pass a bill by this Saturday, before President Obama departs for his international trip. If they are not able to garner enough votes, Democratic leaders have hinted they may employ a parliamentary maneuver dubbed as "deem and pass."
The controversial procedure would allow House members to vote on health care changes without ever voting directly on the Senate bill. In this case, the House would vote on a "fix it" measure that would make changes to the Senate health care bill and then automatically, in the process, pass the bill without actually having to vote on it.
The procedure has been used 20 times over the last 30 years by both Democrats and Republicans, often on technical or unpopular measures like raising the debt limit, but never on one as big as health care reform.
Hoyer today defended the tactic as a "clean up or down vote," even as some question its constitutionality.
"We're going to have a clean up or down vote on the Senate bill, that will be on the rule," Hoyer said. "This is not an unusual procedure. We're going to vote on a rule."
"Unfortunately, the Republicans are a little bit like the boy who killed his two parents and then wants sympathy because they're an orphan. They've tried to stop the passage of this bill, slowed it up," he added. "We'll vote for the Senate bill in the rule, and then we will amend the Senate bill in the process."
Cantor said the House rules allow for the use of this "deeming" provision but charged that the move Democrats are pondering is an attempt to fool the public.
"Again, when you're dealing with a bill like this that will cost a trillion dollars and it will effect health care for every man, woman and child in this country, I don't think you can fool the public," Cantor said on "GMA." "This is an attempt to hide the vote. There's no doubt about it."
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 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 objection from Republicans.
"We will do whatever is necessary to pass a health care bill," said Pelosi, D-Calif.
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.