Democrats, in contrast, held to the line that increased government revenues are key to fixing the problem, and say Republicans are too quick to rule out this piece of the puzzle.
Senate Majority Leader Harry Reid (D-Nev.) even introduced a sense of the Senate bill that calls on people earning more than $1 million a year to "make a more meaningful contribution to the deficit reduction effort."
When members return on July 5, there will be less than one month before the August 2 deadline by which the Treasury Department says the debt ceiling will need to be increased.
With that as an ongoing backdrop, the House and Senate will continue to work its way through a variety of issues, including Libya, Defense Department Appropriations, and an appropriations bill for the Department of Energy and related agencies.
In the Senate, members will meet Tuesday to take up S.J.Res. 20, a resolution authorizing ongoing military operations in Libya.
After that, the Senate's schedule is unclear -- even more so than usual, since Republicans this week twice stopped requests to move to new business until a debt agreement is reached. Continued protests along those lines could make for another noisy week in the Senate.
Senate Republicans are also pressing for a balanced budget amendment to the Constitution, and more debate on that is possible as well.
In the House, members will continue work on the Department of Defense Appropriations bill on Wednesday, and finish on Thursday. On Thursday and Friday, members are expected to start work on the Energy and Water Appropriations Act, and the Flood Insurance Reform Act.
A more detailed look at the week ahead follows:
The House and Senate are out for the Fourth of July holiday.
The Senate returns at 2 p.m. to take up S.J.Res. 20, which would authorize military operations in Libya for one year, or until NATO operations end, whichever comes first. This is similar to a resolution that has already failed in the House.
The House returns at 1 p.m. for a pro forma session; no votes are planned.
The House meets at 2 p.m. for legislative work and will continue work on the Defense Department Appropriations Act, H.R. 2219. The rule for this bill has already been approved, and members are expected to take up amendments by Wednesday.
Votes are expected on two bills under a suspension of House rules. One is H.Res. 268, which reaffirms the U.S. commitment to a negotiated settlement of the Israeli-Palestinian conflict. This is similar to a resolution the Senate has already passed.
The second bill is H.R. 515, the Belarus Democracy and Human Rights Act. This bill criticizes Belarus' human rights violations against its citizens, calls on Belarus to release political prisoners, and calls for new elections in light of what the bill calls the "fundamentally flawed" elections last December.
Thursday and Friday
The energy and water bill would cut more than $1 billion in spending for the Department of Energy and other agencies, and can be expected to meet with Democratic complaints about these cuts.