Vice President Joseph Biden and House Majority Leader Eric Cantor emerged from bipartisan deficit-reduction talks Tuesday sounding far apart on taxes but optimistic about reaching a deal exceeding $1 trillion in savings.

“I made it clear today … revenues are gonna have to be in the deal, and everybody knows that at the end of the day, we’re going to have to make some really tough decisions on some of the big-ticket items,” Biden said.

But he drew stiff resistance from Cantor. “Tax increases are not going to be something we’ll support in the House,” the Virginia Republican said. “I just want to make sure that that point is made very clear.”

But both appeared to agree that the group could achieve more than $1 trillion in deficit reduction. Biden predicted that the group members could “pretty quickly” agree to the amount as a “down payment” and that they would discuss triggers that would achieve a total of $4 trillion.

“Everybody’s still talking to each other, and they’re not talking much to [reporters]. And that is evidence that it’s serious,” he said.

Cantor echoed Biden’s optimism. “I am confident we can achieve over $1 trillion in savings at this point, and hopefully more,” he said. “I do think, also, what this reveals is that actually coming together and finding some agreement on spending cuts is not that difficult.”

Cantor would not give specifics about the ongoing discussions, saying only that the group is talking “in broad numbers.” He added that whatever terms the group reaches would still need to move through the legislative process.

Biden’s group is scheduled to meet again Thursday. The other negotiators are House Budget ranking member Chris Van Hollen (D-Md.), House Assistant Leader James Clyburn (D-S.C.), Senate Minority Whip Jon Kyl (R-Ariz.), Senate Finance Chairman Max Baucus (D-Mont.) and Senate Appropriations Chairman Daniel Inouye (D-Hawaii).

The other negotiators merely issued platitudes about making progress after Tuesday’s meeting. The group also agreed to keep meeting even when one chamber is in recess.

The group is trying to agree on deficit-reduction measures as lawmakers grapple with raising the debt ceiling. The Treasury Department projects that the U.S. government will begin defaulting on its loans Aug. 2, forcing lawmakers to take up the issue before breaking for the summer recess.

“I don’t think anybody wants to wait until the end,” Cantor said, referencing the August deadline. “This place tends to be a place of procrastination. Perhaps this can be different.”

House Republicans are planning to hold a test vote on the debt ceiling debate as early as next week. Although the vote is expected to fail, the move is an attempt to show Senate Democrats and President Barack Obama that significant spending cuts are needed alongside an increase in the debt ceiling.