House Speaker John Boehner said Wednesday that the House "absolutely" will take up the new Senate budget plan -- even if he has to rely on mostly Democrats to pass it -- and that he expects the partial government shutdown to end by Thursday.

Boehner made the comments in an interview with Cincinnati radio station WLW-AM.

"We fought the good fight. We just didn't win," he said.

Boehner spoke as the Senate was preparing to vote on a recently struck bipartisan deal to end the partial government shutdown and raise the debt ceiling.

The Senate proposal would fund the government through Jan. 15, and raise the debt cap through Feb. 7.

More On This...

The plan would not include any provision relating to the ObamaCare medical device tax, as prior plans did; instead it would include a single provision meant to verify the income of those receiving ObamaCare subsidies. It would also instruct a bipartisan budget committee to report back on a broader plan by mid-December.

Lawmakers on both sides acknowledged the deal was far from perfect, and once again pushes off difficult and long-term decisions about the country's fiscal health for another day.

"This deal is yet another promise to work on the problem tomorrow," Sen. Mike Enzi, R-Wyo., said in a statement.

It also tees up another confrontation weeks down the road if the two sides are unable to scratch out a longer-term deal. But, for the near-term, it would lift the partial shutdown that began on Oct. 1 and remove the threat of missing the debt-ceiling deadline on Thursday.

The big question had been whether, if the bill passes the Senate, Boehner would allow it to come to the floor. Though many Republicans remain resistant to the plan -- in large part because it does not significantly address ObamaCare -- it could potentially pass with a combination of moderate Republicans and Democrats.

Asked Wednesday if he'd let the House vote, even if a majority of Republicans wouldn't support it, Boehner said: "Oh, absolutely."

But Boehner added he'll encourage Republicans to support it.

"We fought the good fight. There's no reason for our members to vote no today," he said. Boehner said he anticipates the partial shutdown will be over by Thursday.

Boehner met with his rank-and-file members Wednesday afternoon ahead of the Senate vote. The House is planning to take up the measure shortly afterward. One House GOP leadership aide said it appears there's enough support to pass the bill.

Boehner, in deciding to let the Senate bill come to the floor, had been left with few options.

The night before, Boehner had been forced to shelve his chamber's alternative bill amid resistance from conservatives, and just about every Democrat. Conservatives complained it didn't go far enough in eroding ObamaCare. Already Wednesday, those same lawmakers were being pressured by conservative groups to vote "no" on the emerging deal.

Boehner could have tried to put forward a new proposal, which would easily put the government past Thursday's deadline to raise the debt ceiling.

The other option was simply bringing the Senate bill to the floor, relying on some Republicans and a lot of Democrats to pass it. Despite pressure to oppose the bill from groups like the Club for Growth, moderate Republicans disenchanted with the Tea Party's confrontational approach could peel off and join their Democratic colleagues.

House Democrats were already planning for that possibility. Senior House Democratic sources told Fox News that the party is confident they can deliver most of their caucus on the vote.

The current House breakdown is 232 Republicans and 200 Democrats. That means Republicans need help from Democrats if they lose just 16 members.

House Democrats held a formal meeting Wednesday afternoon, as Senate leaders charged ahead with votes expected later in the day. Sen. Ted Cruz, R-Texas, helped clear the way for that vote when he announced he would not filibuster, though he opposes the deal itself.

White House Press Secretary Jay Carney, indicating President Obama would support the plan, said the president believes it "achieves what's necessary."

The model for a bill being passed largely by Democrats is the vote in January on aid for Hurricane Sandy victims. The House approved it 241-180 -- but with only 49 Republican yeas and a robust 192 Democratic yeas.

The move would be risky for Boehner, and could potentially trigger another effort down the road, from the right, to challenge his speakership. Letting a bill pass on the backs of votes from the minority party would violate what is loosely known as the "Hastert Rule" -- named after former Speaker Dennis Hastert, and referring to the principle that the party in control of the House should make sure that party is mostly on board with any bill coming to the floor.

But would Boehner really be in trouble by relying on Democrats? One senior House Republican said it's "highly unlikely" that a new leader would emerge "that can raise money, message" and corral the warring factions of the party.

"Boehner takes the high road," the aide predicted. "He tried to do the right thing. It's not like he hasn't been warning us."

Since initially demanding that ObamaCare be defunded as part of any budget deal, Republican leaders have scaled back those demands considerably. The boldest provision in the most recent House bill would have forced top government officials and lawmakers onto ObamaCare, without subsidies.

But the latest version was still too heavy-handed for Democrats, and too weak for conservatives. The final version only addressed income verification for subsidies.

Fox News' Chad Pergram contributed to this report.