On Thursday, House Republicans met with President Obama at the White House for a discussion that the GOP described as "useful." The meeting prompted a late-night discussion within the GOP on how to proceed, and ongoing talks were expected.

But as "useful" as the meeting may have been, it wasn't clear how the two sides would work around their essential dispute:

— Republicans want a six-week extension of the debt ceiling, and want to use that time to reach a broader budget agreement. In the mind of the GOP, an agreement here could lead to new spending cuts and would allow the government to reopen.

— Democrats say a broader fiscal negotiation could only happen once the government is open and the debt ceiling is extended.

Even without an agreement in place, House Republicans could decide to move anyway on a bill extending the debt ceiling for six weeks. Stocks soared on news that a debt-ceiling fix was in the works, and the GOP could decide it's important to show it wants to avoid a default on the debt.

Importantly, the White House signaled Thursday that Obama would sign a six-week debt-ceiling extension.

House GOP leaders said it is "possible" that the House considers a debt-ceiling bill today. But as of Friday morning, they had not released any text of a debt-ceiling bill, and that text might be changing in light of the White House meeting.

The one firm item on today's House agenda is the next "mini" spending bill. Members will meet at 9 a.m. and consider H.J.Res. 76, the Nuclear Weapon Security and Non-Proliferation Act.

A vote on that bill should happen by mid-morning. If it passes, it would be the 14th of these narrow spending bills, which Republicans have put forward as a way to reduce the effects of the shutdown.

But it's not all about the House. The Senate is headed toward a procedural vote Saturday on a Democratic proposal to extend the debt ceiling through the end of 2014.

If the vote is held, it would be on a motion to end debate on a motion to proceed to that bill, S. 1569.

Senate Republicans will also get involved today. They meet in the morning with President Obama and are already discussing a plan that seems to be a mirror image of the House GOP plan.

Specifically, Senate Republicans are considering seeking concessions on the debt ceiling increase and are more interested in immediately reopening the government.

The Senate starts work at 10:30 a.m. today, and after some initial remarks, it will recess to allow the Senate GOP to meet with Obama.