Republican and Democratic House leaders offered few specifics Thursday about their first debt limit meeting with Vice President Joseph Biden but said they are optimistic and see areas of commonality with each other.

Majority Leader Eric Cantor said there was “general agreement that things have got to change” and that spending cuts and other budgetary reforms are necessary.

However, the Virginia Republican declined to address where Democrats and Republicans can find common ground.

“I think broadly all of us understand we’ve got to achieve results,” Cantor said, noting that there are some areas in both the Democratic and Republican budget proposals that could be under review.

And while some of his colleagues have hinted that the House Republicans’ Medicare plan could go on the chopping block as part of the negotiations, Cantor said that for him it was “still on the table.” The Medicare proposal is a non-starter in the Democratically controlled Senate.

“This president has done nothing but attack the plan in the Budget chairman’s document and that’s unfortunate because I think today’s meeting really was in contrast to the rhetoric that we’ve heard before,” Cantor said.

Assistant Leader James Clyburn also said he was “very optimistic” that the committee could reach a deal on both the budget and the debt limit.

The South Carolina Democrat echoed Cantor’s description of the meeting as collegial.

“This is not Democratic versus Republican. This is a Congressional committee that is trying to work through some very difficult issues,” Clyburn said.

Still, Clyburn refused to discuss where areas of agreement can be reached.

“Nobody locked themselves into anything,” he said. “We’re open to everything.”

The comments come after Congressional negotiators met for two hours Thursday morning at Blair House, near the White House. Biden put out a statement that progress had been made and negotiations would resume Tuesday.

“On behalf of all of us, let me say, we had a good, productive first meeting today,” Biden said in a statement. “We plan to meet again on Tuesday and look forward to further discussions on these important challenges.”

President Barack Obama requested that Biden conduct the meetings with negotiators appointed by Congressional leaders of both parties as a way to try to avoid a potentially catastrophic default on the nation’s debt obligations. Treasury Secretary Timothy Geithner has said the nation will default on its loans by Aug. 2 if Congress does not raise the debt limit before then.

Congressional lawmakers in attendance were Cantor, Senate Minority Whip Jon Kyl (R-Ariz.), Clyburn, House Budget ranking member Chris Van Hollen (D-Md.), Senate Finance Chairman Max Baucus (D-Mont.) and Senate Appropriations Chairman Daniel Inouye (D-Hawaii).