Given this week's unraveling of the talks, a debt ceiling deal now appears likely to be the top priority of the White House and Congress for the next month. All the same, other issues are piling up, chief among them military action in Libya.

The Senate Foreign Relations Committee on Tuesday will hold a hearing on a proposal from Committee Chairman John KerryJohn Forbes KerryBringing the American election experience to Democratic Republic of the Congo Some Dems sizzle, others see their stock fall on road to 2020 The Hill's 12:30 Report MORE (D-Mass.) to authorize continued operations in Libya.

But even if the Senate ultimately approves that resolution, the House already rejected a similar measure on Friday. In addition, members of the House will push for a full defunding measure once they return.

The Senate's day-to-day work is still expected to dodge these larger issues. The Senate has loosely scheduled some debate on a bill next week that would alter the presidential appointment process. Several amendments are "pending" to that bill, but it's unclear which will come up for a vote.

Meanwhile, the House passed two bills this week that could require the Senate to act, and might even force a House-Senate conference.

On Friday morning, the House approved a controversial patent reform bill, which is similar to one the Senate approved earlier this year. If the Senate agrees to a conference on this bill, it may mark one of the rare times this year the two bodies hold an old-school conference meeting to reconcile the bills.

Also this week, the House approved a bill to extend the Airport and Airway Trust Fund until late July. This fund, which is a significant source of revenue for the Federal Aviation Administration, expires June 30, and the Senate can be expected to approve the bill sometime next week. (A longer-term FAA extension is already the subject of a conference committee process, but this has been long stalled over what Democrats say is anti-union language.)

Far less certain is whether the Senate has any plans to take up the FY 2012 spending bills that the House is methodically churning out. When the House returns in July, work starts on the Defense spending bill.

The Senate returns to work Monday, June 27, at 2 p.m.