Why is John A. Boehner so calm?

As a potential government shutdown looms next week, it’s the most important question on Capitol Hill. The fate of the federal budget — and the momentum of a Republican resurgence — could depend on whether the new House speaker is just faking confidence or is about to Houdini his way out of a political jam.

Boehner’s problem is that some outspoken Republicans think the key to this year’s budget fight is not solving it but fighting it the right way. They won’t budge from demands for deep spending cuts.

Boehner (R-Ohio), on the other hand, will be judged on the end of this fight, not its means. He wants to avoid a shutdown and has negotiators working on a deal that would include about $33 billion in cuts.

The speaker looks like he will have trouble either way. If he compromises with Democrats, he could put himself at odds with the conservatives who were supposed to help him reshape government. If he doesn’t, he could look like he has failed to govern at all.

Of course, all of this could be part of a grand strategy that will leave the government smaller, the Republicans united and Boehner firmly in charge.

If so, the speaker has one week to reveal it.

“I want to try to energize him,” said Rep. Allen B. West (R-Fla.), one of 87 freshmen, talking about the speaker he helped bring to power. “To let him know that, ‘Just get out there, and try a little harder.’ ”

Trying to explain Boehner’s position so far, West thought of a battle scene in the movie “Braveheart” in which Scottish nobles seek to negotiate with their enemies. William Wallace, Mel Gibson’s rebel character, rallies the Scottish army to fight instead.

Boehner is acting like the nobles, West said. That would make West, in office for four months . . . Braveheart.

“They won that battle,” West said.

Outwardly, Boehner looks like a man in control. On Friday, at T-minus seven days, he was still loose enough to joke with reporters. “You probably all think we’re going to have a press conference. April Fools’,” he said.

Boehner feigned leaving the podium, then returned.

“There is no agreement on a number. We’re going to fight for the largest spending cuts that we can get,” he said.

Boehner said it was important to get the current budget fight resolved, “so that we can get on with the big issues ahead of us,” including debates over next year’s budget and an increase in the federal debt limit.

In private, aides said Friday that Republicans and Democrats were still working toward the same kind of deal that Vice President Biden outlined earlier in the week. That would include about $33 billion in spending cuts — slightly more than half of the $61 billion that the Republican-led House approved in February.

The full text of an agreement might not be ready until the middle of next week, leaving just days to approve it.

If Republicans defect, Boehner would be left with two possible ways out, each with its own costs. He could persuade unhappy Republicans to vote yes and move on. Future spending bills could give them a new chance to attach controversial riders cutting funds for Planned Parenthood, NPR or the Environmental Protection Agency.

“He has a personal relationship with every member of the House Republican Conference and certainly isn’t going to write off any of them or their concerns in the discussions,” a spokesman for Boehner said in a statement.

At times this year, the freshmen have voted as a unified bloc. At other times, they have fractured: During a vote on the last stopgap budget, 75 percent of the freshmen voted yes.

On Friday, some freshmen said they were reserving judgment until they saw a budget deal and were open to removing some of the riders.

“We can deal with those another day,” said Rep. Steve Southerland II (R-Fla.).

But Rep. Joe Walsh (R-Ill.) said he needed all the cuts, and all the riders: He would support only a compromise that was not a compromise at all.

“It’s important that we succeed in this initial fight,” Walsh said.

He added that ultimately Boehner, not him, will be persuaded to change his views. “The American people are behind him on this,” Walsh said. “I think he’s starting to realize that.”

Boehner also could work around rebellious freshmen and find votes from House Democrats. On Friday, anticipating that kind of deal, Democratic Rep. Peter A. DeFazio (Ore.) was already on the House floor, telling the newcomers they’d been bamboozled.

“Let’s keep the Republican freshmen busy, while behind closed doors your speaker is cutting a deal!” DeFazio said. “Things haven’t changed around here all that much.”

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