One of them will have to blink.

In the coming debt-ceiling debate, President Barack Obama and Speaker John A. Boehner will face another test of wills over fiscal policy — and the “Boehner rule” could be a linchpin that will either set the tone for the remainder of Obama’s term, if Boehner has his way, or be a thing of the past, as the president hopes.

The weakened speaker — who survived an aborted coup attempt by insurgent Republicans last week — is clinging to the rule he coined in 2011 that every dollar in debt ceiling increase be matched by a dollar of “spending cuts and reforms.”

But Obama vows he will no longer negotiate for the debt ceiling “hostage” — even as he makes a demand of his own. He wants any new spending cuts to be accompanied by even more tax revenue than the $620 billion he secured during the fiscal cliff negotiations.

To the extent that there is wiggle room, Boehner hasn’t put a time limit on when spending cuts must take place, and most of the entitlement changes he is seeking — such as increasing the Medicare eligibility age — would have much bigger effects in future decades.

Plus, the president continues to say he wants a longer-term debt and deficit deal that would include new spending cuts, but so far he hasn’t proposed enough to comply with the spirit of the Boehner rule. But two years of on-again, off-again grand bargain talks haven’t yielded a breakthrough, and there’s no indication yet that they will finally be able to consummate such a deal anytime soon.

The White House’s Talk-to-the-Hand Strategy

Ever since re-election, the president has been flexing a tougher negotiating strategy unburdened by election worries. But even though Democrats repeatedly said they were prepared to let the nation go over the cliff if Republicans didn’t agree to their myriad demands on taxes, spending and the debt ceiling, many Democrats, and some Republicans, viewed the White House as having flinched in agreeing to a limited deal involving tax hikes.

Still, the White House is essentially daring Republicans this time to shoot the debt limit hostage, under the assumption that it would be political suicide for the GOP. After all, a default on the debt is widely predicted to result not just in a downgrading of the U.S. debt but also a worldwide recession.

Many Democrats ended up voting for the fiscal cliff deal after Vice President Joseph R. Biden Jr. vowed that Obama would not negotiate on the debt ceiling and that Republicans would cave.

Biden argued that business leaders would lobby Republicans and that the Wall Street Journal editorial board would also bring pressure to bear.

Press Secretary Jay Carney repeated Monday that the White House was more than happy to discuss a long-term solution to the nation’s debt and deficit issues — including averting the automatic $1.2 trillion in sequester cuts looming in March and more tax hikes on the wealthy.

In the meantime, Carney warned that the White House simply would not engage in negotiations with the GOP on the debt ceiling.

“Congress racks up the bills. … The president will not negotiate with Congress over Congress’ responsibility to pay its bills,” Carney said.

So far, the administration hasn’t offered up a fallback plan if Congress refuses to act. Carney last year disavowed using the 14th Amendment’s provision against questioning the federal debt as a way to declare the debt ceiling invalid. Nor has the administration commented yet on a scenario popular among bloggers and some liberals such as columnist Paul Krugman and Rep. Jerrold Nadler, D-N.Y. — using the Treasury secretary’s authority to mint platinum coins in any denomination as an end run around Congress. Mint a few $1 trillion coins to pay the bills, and the problem could be kicked to the next administration.

As the nation inches closer to a default — possibly by the end of February — expect the White House to ratchet up the pressure by pointing to all of the bills that would go unpaid, even if debt interest payments are covered. The government would need to cut spending by about $100 billion a month — enough to cause an instant recession were it to last any length of time — while potentially blowing holes in the budget of every agency, contractor, state government and recipient of federal benefits such as Social Security.

The GOP’s Threatening-to-Shoot-the-Hostage Strategy

For as much as the White House says Democrats won’t negotiate around the debt limit, congressional Republicans believe Obama will in the end have to come to the table, which, in their minds, means he’ll have to agree to more spending cuts.

Boehner and Senate Republicans have been clear about using the debt limit to exact more spending cuts from the White House. And perhaps the key player in this latest debt ceiling hostage crisis will be Minority Leader Mitch McConnell, R-Ky., who has been central to every budget deal for the past two years.

“If the president won’t lead us here in the direction of reducing this massive spending addiction that we have, then we have to use whatever leverage we have,” McConnell told CBS News on Sunday.

Multiple GOP aides conceded that these next few weeks will be critical for the party in trying to gain an upper hand for the battle in February or March. With income tax rate hikes permanently set on the wealthy, Republicans view Obama’s renewed push for revenue as moot, and they want to turn to entitlement cuts.

“He doesn’t have a choice — he can declare whatever he wants to declare, but he needs to pass one,” one top Senate Republican aide said of a debt ceiling bill. “If [the White House] had shown any interest in dealing with spending and debt, we would not have to use the debt ceiling or anything else as leverage.”

Rank-and-file members are largely on board with where leadership is taking them, even if they were less than pleased with the tax deal that helped avert, at least partially, the fiscal cliff Congress created. Though many voted for the Jan. 1 deal, their “yes” votes will come much less easily on the debt limit, which many of them do not feel obligated to extend.

“[Obama] says he won’t negotiate to raise the so-called debt ceiling … I have a message for him: That’s not going to happen,” Sen. Orrin G. Hatch, R-Utah, wrote in an op-ed Monday. “If he thinks I’m going to agree to more revenue so he doesn’t have to cut spending, he’s got another thing coming.”