Boehner, R-Ohio, is under increasing pressure to come up with a budget that satisfies his party's conservatives and can still pass the chamber, Roll Call reported Wednesday.
"There's a lot of pent-up demand from our members to show the American people a way forward to fiscal sanity ... and we're going to do that," Boehner said.
Republican leaders and GOP members of the Budget Committee are meeting behind closed-doors this week to see if they can set budget levels below what appropriators have said they need for passage.
House Budget Chairman Paul Ryan, R-Wis., said he doesn't know where the spending cap will fall.
Political observers say it is unlikely the number will go quite as low as the $931 billion that some have called for.
"You get a number low enough, and you'll get conservatives voting on it," said Rep. Mick Mulvaney, R-S.C.