The agreement would provide an extra $80 billion,. divided evenly between the Pentagon and domestic agencies over the next two years, and extend the government's authority to borrow to pay bills into March 2017, as Obama's successor settles into the White House.
Approval would reduce the chance of partisan fights cascading into a federal shutdown or default, a relief to Republicans fearing such events would alienate voters.
A foremost beneficiary would be Ryan, R-Wis., the 2012 GOP vice presidential candidate, who seemed certain to be nominated as speaker when House Republicans vote Wednesday. Boehner had said he wanted to "clean the barn" of politically messy issues so Ryan, 45, could make a fresh start.
Ryan mostly ducked reporters seeking Tuesday to hear his views on the budget package and his role, if any, crafting it.
He said only that the secret, top-level process that party leaders and the White House used to reach the accord "stinks" and promised not to operate that way as speaker. Spokesman Brendan Buck said Ryan, who chairs the House Ways and Means Committee, played no part in the negotiations.
Ryan's promise echoed demands of the outsider-oriented conservatives who made Boehner's life miserable because they felt he left rank-and-file lawmakers powerless. But Ryan still faces tricky consequences, no matter how he votes on the budget compromise.
If he opposes it, he would look oddly out-of-step with the same establishment Republicans who virtually browbeat him to seek the speaker post. But if he supports it, he could get off to a poor start with the roughly 40 members of the Freedom Caucus, most of whom voiced support for him last week after initially backing a long-shot rival, Rep. Dan Webster, R-Fla.
The full House is scheduled to formally elect Ryan as speaker Thursday.
There was only slightly more suspense over the budget agreement. One conservative leader, Rep. Bill Flores, R-Texas, predicted the compromise would get 70 to 90 GOP votes, which seemed sufficient for passage when combined with what is expected to be solid support from Democrats.