The Post reports this morning that freshmen House Republicans are under intense pressure to vote to raise the federal debt limit. In truth, the real pressure is now on Speaker John Boehner to deliver dramatic spending reductions in exchange for any debt-limit increase — thanks to the ever-shrinking budget deal he cut with President Obama.

When it emerged that the agreement will reduce actual federal outlays by just $352 million this fiscal year, conservatives were infuriated. The agreement has produced a breach of trust between Republican leaders and their troops — on Capitol Hill and across America. Rep. Allen West (R-Fla.), a Tea Party favorite, spoke for many when he declared: “Character and integrity are important things with me. I like people to be upfront with me. Surprises are for birthdays. When you wake up, and all of sudden . . . it is really only $352 million in cuts, I don’t like that.” Neither do the voters who powered the GOP to victory last November and put Boehner in the speaker’s chair.

Boehner should have told his caucus and its grass-roots supporters the truth: This was the best he could do under the circumstances. Unlike 1995, when Congress had already passed a defense appropriations bill, this time around a government shutdown would have left our troops without paychecks. Republicans would have been pilloried if they were seen as withholding pay for our deployed forces in a time of war, leaving their families back home unable to make ends meet. Boehner led a congressional visit to troops in Iraq this weekend. Imagine the reception the GOP members would have received if the speaker had not reached a deal.

Considering his lack of leverage, Boehner actually achieved a lot. He denied Obama the $40 billion spending increase the president had demanded, secured some real spending cuts and — in a little-noticed but important victory — restored school choice in the District of Colombia. A defense of these achievements — with a promise to demand much more in the debt-limit fight — would have been better than selling this agreement as something it is not.

Unfortunately, the speaker continues to do just that. In the face of mounting criticism on the right, Boehner dug in last week, declaring “There are some who claim that the spending cuts in this bill aren’t real, that they’re gimmicks. Well, I just think that is total nonsense.” Each time he makes this argument, he compounds the damage. Conservatives are not buying it, and they are putting Boehner on notice. National Review called the budget deal “strike one against the speakership of John Boehner.”

Boehner will get another swing at the ball in the debt-limit fight. He will enter those negotiations with his base, and his caucus, watching him with wary eyes. They know that he has much greater leverage in this fight — and will be expecting much bigger results.

One thing Boehner must not do is to pass a debt-limit increase the way he passed the budget deal last week — by relying on Democratic votes. A quarter of the GOP caucus voted “no” on the agreement. Boehner pushed it though with a “75-40” coalition (75 percent of the GOP caucus and 40 percent of Democrats). He will face an uproar on the right if he tries that on the debt limit. If one-in-four Republicans won’t vote for the debt-limit deal he cuts, the speaker will have failed. He needs to make bold demands and stick to them. If Obama refuses to make a deal, Boehner should make clear that the House will begin passing small debt-limit increases that are just enough to keep the government solvent for a few weeks at a time — and will attach deep spending cuts to each one. Obama cannot veto such temporary measures. The message to the president should be: We can cut spending the easy way or we can do it the hard way, but there will be no debt-limit increase without major spending reductions and reforms.

Doing this will require great spinal fortitude, but Speaker Boehner has a lot to prove. The only thing worse than continuing to defend the current budget deal would be for Boehner to cut a bad deal when it comes to the debt limit.

Marc A. Thiessen, a visiting fellow with the American Enterprise Institute, is the author of the book “Courting Disaster” and writes a weekly column for The Post.