Sens. Patty Murray (D-Wash.) and Sen. Jon Kyl (R-Ariz.) chat as Sen. Pat Toomey (R-Pa.) walks past after the supercommittee meeting Tuesday. (Mike Theiler/REUTERS)

Members of the bipartisan joint committee tasked with finding $1.5 trillion in deficit savings over the next decade revealed few details Tuesday after their second closed-door meeting.

Addressing reporters after the 2 1/2 - hour meeting, the panel’s co-chairs, Sen. Patty Murray (D-Wash.) and Rep. Jeb Hensarling (R-Tex.), said only that the 12-member group was making progress.

"We had a very productive conversation today," Murray said after the meeting, which took place in a conference room of the Library of Congress Jefferson Building just east of the Capitol. "Clearly, we all understand the tremendous time challenge in front of us and the tremendous challenge on the part of our country today for us to come to an agreement. We had a great discussion today to begin to frame that, and we will continue to move forward."

Hensarling said that “every day that the committee meets, I believe there is progress.”

"I think members understand how serious the situation is with respect to both our debt crisis and our unemployment crisis,” he said. “Every member is still committed to achieving success. We're making progress and we look forward to our hearing on Thursday."

The panel holds its third public meeting Thursday, and is expected to take up the issue of comprehensive tax reform. Tom Barthold, chief of staff for the Joint Committee on Taxation, will testify.

Sens. Pat Toomey (R-Pa.) and Jon Kyl (R-Ariz.) were the first to leave Tuesday’s meeting. They were followed by Sens. John Kerry (D-Mass.) and Max Baucus (D-Mont.). Then the three House Democratic members on the panel – Reps. Chris Van Hollen (Md.), Xavier Becerra (Calif.) and James Clyburn (S.C.) – departed, followed by Sen. Rob Portman (R-Ohio). Murray and Hensarling were the last to leave; Reps. Dave Camp (R-Mich.) and Fred Upton (R-Mich.) did not pass by reporters on their way out.

The White House and congressional leaders – as well as several members of the committee – have pushed for deficit savings in excess of the panel’s $1.5 trillion mandate. But the supercommittee’s work has been made tougher in recent days by competing demands from President Obama and House Speaker John Boehner (R-Ohio).

Boehner said in a speech last week that tax increases should not be included in a final deal, while Obama said in a Rose Garden address on Monday that he will veto any deal that includes entitlement cuts but no fresh revenue.

Asked Tuesday whether House Republicans favor a “grand bargain” in the ballpark of the $4 trillion goal of previous bipartisan debt-reduction efforts, House Majority Leader Eric Cantor (R-Va.) noted that the House GOP’s fiscal 2012 budget proposal, which was not enacted, called for “over $6 trillion in savings.”

“If you want to talk about what we want, absolutely, we want to see real tax reform,” Cantor said. “We put forward in our budget real entitlement reform that actually is a multi-generational fix in entitlement reform. The president is not interested in that. He said now he is not even interested in kicking the can, which is the age-adjustment. Again, I would ask where is the leadership on that?”

Cantor added that his hope was that the supercommittee would at least reach its goal as mandated in last month’s debt-ceiling deal, and suggested that the work of the bipartisan group led by Vice President Biden in the spring “certainly could provide a starting point.”