The fine print in the deal to raise the debt limit scares the daylights out of defense hawks — and even some middle-of-the-roaders on Pentagon spending — and not without reason.

Here’s how it’s supposed to work: Assuming passage of the first round of spending cuts, a joint bipartisan committee will set to work on recommendations for a second round, negotiating for about four months before reporting back. If the committee reaches agreement, great. If it doesn’t, a “trigger” mechanism kicks in.

And that trigger mechanism would force automatic across-the-board cuts of $1.2 trillion to agency budgets over the next decade, split half and half between domestic programs and defense.

To put that $600 billion in perspective, it’s worth noting that the federal government was already looking at reducing projected spending on national security by about $400 billion over the next 12 years. That has prompted the Pentagon to initiate a “comprehensive review” of its spending and, in doing so, to confront huge questions about how to trim costs while recalibrating the military’s ambitions.

The question now is what even bigger cuts might mean.

Last week, Army Gen. Martin Dempsey, President Obama’s nominee to be chairman of the Joint Chiefs of Staff, was asked at his confirmation hearing what a proposal to cut, say, $800 billion over the next decade would mean for military readiness.

“Based on the difficulty of achieving the $400 billion cut, I — I believe $800 billion would be extraordinarily difficult and very high risk,” Dempsey replied.

And, indeed, defense hawks do see something approaching apocalypse.

“While the trigger mechanism comes into play only if the Congressional negotiators fail to reach agreement on the second phase of spending cuts, it verges on catastrophe to take such a national security risk,” John Bolton, ambassador to the United Nations under President George W. Bush and now a senior fellow at the American Enterprise Institute, wrote even before Sunday night’s deal was done.

There are some defense experts who don’t see the situation as quite that bleak. Even if it would mean a reduction in personnel, that reduction would come as the war in Afghanistan winds down. And spending reductions overall would represent a much smaller percentage decline then the Pentagon undertook at the end of the Cold War.

“It’s not like it would be whacking America’s defense budget to the bone,” Gordon Adams, who oversaw national-security budgets for the Clinton White House, told The Post this month, when the Pentagon was already bracing itself for cuts exceeding $400 billion.

The hope among many at the Defense Department — and on Capitol Hill — is that the joint bipartisan committee can strike a deal that spreads around the pain just enough to win agreement, and that the Pentagon won’t end up bearing an outsized burden.

That’s the White House’s hope, too. The president “has not called for and would not support these kinds of cuts in defense spending,” press secretary Jay Carney said Monday.

For now, however, there’s at least some fear that the Pentagon might get whacked. “I am very concerned about the defense spending side of it. I wouldn’t have put that in there,” Sen. John McCain (R-Ariz.) told CBS’s “Early Show,” adding that he “probably will have to swallow hard” before voting for the measure to raise the debt ceiling.

That said, McCain, like the White House, is hoping for compromise.

“I also believe that it won't come to that, in that I believe that this select committee, they’ll come up with some pretty good and viable solutions,” he said. “I'm convinced.”