A week before his inaugural, President Obama says he won’t negotiate with Republicans over raising the debt limit.

At an unexpected news conference on Monday he said he won’t trade cuts in government spending in exchange for raising the borrowing limit.

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“If the goal is to make sure that we are being responsible about our debt and our deficit -- if that’s the conversation we’re having, I’m happy to have that conversation,” Obama said. “What I will not do is to have that negotiation with a gun at the head of the American people.”

Well and good. But what, exactly, is the president’s strategy when the debt ceiling has to be raised, if the GOP hasn’t relented?

He’s ruled out an end-run around the GOP.

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The White House said over the weekend that the president won’t rely on the 14th Amendment, which arguably gives him authority to raise the debt ceiling on his own.

And his Treasury Department has nixed the idea of issuing a $1 trillion platinum coin that could be deposited with the Fed, instantly creating more money to pay the nation’s bills.

In a pinch, the Treasury could issue IOUs to the nation’s creditors — guarantees they’ll be paid eventually. But there’s no indication that’s Obama’s game plan, either.

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So it must be that he’s counting on public pressure — especially from the GOP’s patrons on Wall Street and big business — to force Republicans into submission.

That’s probably the reason for the unexpected news conference, coming at least a month before the nation is likely to have difficulty paying its bills.

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The timing may be right. President Obama is riding a wave of post-election popularity. Gallup shows him with a 56 percent approval rating, the highest in three years.

By contrast, Republicans are in the pits. John Boehner has a 21 percent approval and 60 percent disapproval. And Mitch McConnell’s is at 24 percent. Not even GOP voters seem to like Republican lawmakers in Washington, with 25 percent approving and 61 percent disapproving.

And Americans remember the summer of 2011 when the GOP held hostage the debt ceiling, bringing the nation close to a default and resulting in a credit-rating downgrade and financial turmoil that slowed the recovery. The haggling hurt the GOP more than it did Democrats or the president.

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But Obama’s strategy depends on there being enough sane voices left in the GOP to influence others. That’s far from clear.

Just moments after the president’s Tuesday news conference, Senate Republican leader Mitch McConnell called on Obama to get “serious about spending,” adding that “the debt limit is the perfect time for it.”

And House Speaker John Boehner said “the American people do not support raising the debt ceiling without reducing government spending at the same time.”

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The 2012 election has shaken the GOP, as have the post-fiscal cliff polls. Yet the Republican Party may not care what a majority of Americans think. The survival of individual members depends on primary victories, not general elections — and their likely primary competitors are more to the right than they are.