The Republican representative from Virginia rejected the bill released by the White House Monday, which proposed fixes to the Senate health care bill passed Christmas Eve and retained many of the same measures.
"This bill is a non-starter," Cantor said on "Good Morning America" today. "The American people right now are the losers in all of this because the signals coming out of the White House don't bode well for positive health care reform.
"The president insists on bringing back a bill that the American people have resoundingly rejected," he said.
"What you can't do just yet is read about the Republicans' consensus plan, because so far they haven't announced what proposal they'll be bringing to the table," White House communications director Dan Pfeiffer said in a blog posted at 5 a.m. on the White House Web site.
"After a year of historic national dialogue about reform, it's time for both sides to be clear about what their plan is to lower costs, hold insurance companies accountable, make health insurance affordable for those without it and reduce the deficit."
Cantor said the idea that Republicans haven't put forth a plan, or are offering only piecemeal solutions, is simply untrue.
"House Republicans have had a plan posted since the vote in the House in July," the No. 2 House Republican said. "We have a better way. We had a vote on our plan and it's a plan that is focused very squarely on bringing down costs and health care costs for the American people."
"Our House bill is validated by the Congressional Budget Office and will bring down health care insurance premiums," Cantor said, referring to the House Republicans bill.
The House Democrats passed their health care legislation Nov. 7. The Republican House leadership released an outline of its proposals in July, but the health care bill is dated Nov. 3. At the time, Democrats criticized GOP leaders for crafting their bill behind closed doors and not being transparent, even within their own party.
The CBO estimated that the House GOP plan would reduce premiums by 10 percent but only cover an additional 3 million people, compared with 31 million in the Senate Democratic plan. Unlike the Democrats, House Republicans do not want to make health insurance mandatory for all Americans nor do they want to offer an insurance-exchange mechanism.
Republican lawmakers have at least three different proposals on the table, of which the House Republican plan is one.
Cantor said what the GOP leadership will be looking for at Thursday's summit is whether the president is open to listening and incorporating Republican ideas on health care overhaul.
"Will he join us in a bipartisan way to try and accommodate the things that most Americans can support, which is focused on bringing down health care costs," he said.
But when asked if he saw any grounds for a bipartisan bill, Cantor said he is skeptical about whether a bipartisan agreement can be reached.