Congressional leaders on Wednesday wrapped up their second deficit-reduction meeting this week with Vice President Biden as Senate Democrats began to seize on a vote on repealing ethanol subsidies as a sign that some Republicans are breaking with their party’s orthodoxy against tax increases.

Lawmakers who left the meeting with Biden at the Capitol offered few details of what was discussed but said they remain hopeful that a deficit-reduction deal can be reached ahead of an Aug. 2 deadline set by the Treasury Department.

“We discussed a lot of things today,” House Assistant Minority Leader James Clyburn (D-S.C.), one of the six congressional negotiators, told reporters after the talks. Clyburn said he’s “very optimistic” the group will work out a deal on a deficit-reduction plan in exchange for a vote on raising the $14.3 trillion federal debt ceiling, but declined to give any further details.

House Majority Leader Eric Cantor (R-Va.), who is representing House Republicans in the talks, told reporters afterward that the group had had a “very, very fruitful discussion” but similarly declined to discuss the specifics of the latest meeting.

“We’re working forward and trying to produce a result, and the secretary of the Treasury stands by his Aug. 2 deadline by which Congress has got to act,” Cantor said.

Office of Management and Budget Director Jack Lew, who along with Biden, Treasury Secretary Tim Geithner and National Economic Council Director Gene Sperling is representing the Obama administration in the talks, said after the more than two-hour meeting only that members are continuing to work through the issues.

“Conversations continue to be in the same constructive spirit,” Lew said. “Everyone’s very focused on the importance of the work we’re doing.”

The working group, which includes Biden, Cantor, Clyburn, Senate Majority Whip Jon Kyl (R-Ariz.), Senate Finance Committee Chairman Max Baucus (D-Mont.), Senate Appropriations Committee Chairman Daniel Inouye (D-Hawaii) and Rep. Chris Van Hollen (D-Md.), will meet again at the Capitol at 1 p.m. Thursday.

The session came a day after a majority of Republicans in the Senate voted to advance a plan to cancel billions of dollars in annual tax credits for ethanol blenders. The proposal didn’t get the 60 votes needed to overcome a filibuster threat, but was backed by 34 of 47 Republicans.

On a conference call Wednesday afternoon, Sen. Charles Schumer (D-N.Y.), the Senate’s number-three Democrat, and Sen. Robert Menendez (D-N.J.) made the case that the vote is a sign of openness among some Republicans on the issue of tax increases. They urged Republicans to go even further in repealing tax subsidies for big oil companies.

“Yesterday, in a remarkable turn of events, 34 Republicans voted to end taxpayer subsidies to ethanol blenders. ... If you think ethanol subsidies are a waste, there’s no way you can justify handouts for oil companies that have seen record profits,” Schumer said.

As for the scope of an eventual debt-ceiling increase – which could be as short as a few months or as long as two years or more – Schumer declined to give specifics but said that Senate Democrats “certainly would like to do this longer-term rather than shorter-term.”

Even as Democrats are seeking to leverage Tuesday’s ethanol vote, a fissure on their own side of the aisle has appeared in recent days as Sen. Joe Lieberman (I-Conn.), who caucuses with Senate Democrats, wrote a Washington Post op-ed expressing support for some Medicare benefit cuts and for raising the Medicare eligibility age from 65 to 67. Democratic leaders have strongly opposed such changes.

Asked Wednesday about Lieberman’s position on Medicare, Schumer said he believed most Democrats disagree with Lieberman on the issue.