But it would delay a discussion on how to deal with the next round of sequester cuts, and create a House-Senate budget conference that would leave until later the chance of the GOP winning new spending cuts.

That raises the chance that House Republicans will balk at the agreement on Tuesday, leaving it unclear how Congress proceeds with just two days left before the government hits the debt ceiling.

It's also unclear if any Senate Republicans would try to delay passage of the deal in the upper chamber.

Once again, the ongoing discussions will lead to a short legislative day. The Senate meets at 10 a.m., and then recesses in the middle of the day for the usual caucus lunches.

The House starts at 10 a.m. for speeches, and then at noon to work on just one spending resolution: H.J.Res. 83, the Impact Aid for Local Schools Act.

This would be the 16th House-passed narrow spending bill, which represent the GOP's attempt to reopen parts of the government during the shutdown, which today enters its third week.

GOP leaders also left open the possibility that some vote may happen Tuesday related to the debt ceiling. But depending on how the day goes, that could mean anything — including passage of the GOP's preferred six-week debt ceiling extension, or passage of no bill at all.

As of Monday night, the House Rules Committee had not released the text of any debt ceiling bill, although it has the ability to quickly convene to approve a rule and start debating the rule on the bill immediately on the House floor.