But the Ohio Republican stopped short of saying majority Republicans needed Democratic support to get the measure through the lower chamber and over to the Senate.
Tea Party conservatives in Boehner’s conference are balking at the funding plan, saying it doesn’t do enough to push back on President Obama’s executive action on immigration.
“I expect it will have bipartisan support to pass the omnibus appropriation bill,” Boehner told reporters at a news conference.
The federal government will shut down on Dec. 11 unless Congress acts first to prevent it.
House Democratic leaders on Thursday declined once more to play their cards in the year-end government funding debate.
"We haven't seen what the Republicans are proposing. When we do, we'll have a comment on it," House Minority Leader Nancy Pelosi (D-Calif.) said during a press briefing outside the Capitol.
The Democrats are laying low and weighing their options, while GOP leaders try to rally support behind Boehner's two-tiered approach to keeping the government running.
The Republicans' strategy would fund most of the government through September but attach a much shorter leash to the Homeland Security Department (DHS), which will implement President Obama's new executive action halting deportation for millions of immigrants living in the U.S. illegally.
The idea is to empower Republicans to return to the DHS funding issue early next year, when the GOP will control the Senate and a larger part of House. But a number of conservatives are vowing to oppose the "cromnibus," arguing that Congress shouldn't fund a program they deem unconstitutional for even another day.
Rep. Steny Hoyer (Md.), the Democratic whip, has remained open to the GOP bill, though he seemed to close the door on it slightly on Thursday.
"We don't think that's the best policy," Hoyer told reporters. "Sen. [Lindsey] Graham — as you know, a Republican senator — said the bill wasn't a good idea. And I agree with that. We'll see what they're going to offer."
Boehner's troubles in moving the bill grew on Thursday, when Heritage Action, an influential conservative policy group, urged Republicans to oppose the GOP package.
“The fight is now, not next year," said Mike Needham, Heritage Action’s chief executive officer. "Americans expect real action, not a show vote.”
Hoyer said he's spoken to Rep. Kevin McCarthy (R-Calif.), the majority whip, about the cromnibus bill. But he declined to say whether the Republicans are asking the Democrats for votes.
"McCarthy and I have talked," Hoyer said. "I don't want to say he's reached out to me for votes, but we've talked about it."
Asked if he thinks Republicans would need Democratic votes to pass the bill, Hoyer said simply, "I don't know."
Pelosi, for her part, said she's spoken to Boehner in search of a bipartisan agreement. But she declined to lend details about what package would satisfy the Democrats.
"I have reached out to the Speaker and said … we want to work together to pass a bill to keep government open," Pelosi said.
"As we had to supply the votes last year to open up government, let us supply the votes to keep government open," she added. "But we can't do it unless we have a bill that is worthy of our support."
GOP appropriators are expected to unveil their spending package on Monday.