But the series of meetings has been increasingly downplayed throughout the week as a near-meaningless gesture, as it doesn't seem likely to resolve the intractable positions of both parties that were seen during Tuesday's dueling budget announcements.
After the meeting, the House will start legislative work at noon by taking up legislation that aims to override the Obama administration's attempt to undermine a key welfare reform provision from the 1990s.
Republicans will call up H.R. 890, the Preserving Work Requirements for Welfare Programs Act. The bill is a response to the administration's effort to waive the current requirement that welfare recipients look for work.
House Republicans say the administration has no authority to waive that welfare-to-work requirement, and that waiving it would remove an important incentive that they say has led to reduced welfare rolls.
Debate is expected to become heated, as Democrats have argued that the waiver is meant to give states the flexibility to set up innovative programs that help people find work faster.
The House will vote on the rule for the bill in the early afternoon — the rule allows no amendments. By early evening, the House should be able to pass the bill.
The Senate meets at 9:30 a.m., and may simply hold light debate on the 2013 spending resolution as it waits for Thursday.
Senate Majority Leader Harry Reid (D-Nev.) on Tuesday filed a motion to end debate on a motion to proceed to the continuing resolution for the rest of 2013. That motion was filed after some Republicans said they needed more time to read a bipartisan alternative to the House-passed continuing resolution, H.R. 933.
If there's no agreement to speed up the time, a vote on this motion would take place Thursday. An agreement could let the procedural happen Wednesday, although the process could get bogged down by requests from senators to allow consideration of amendments.