Congressional Republicans know they can’t stop a tax increase — but they’ll be damned if they let President Barack Obama get a debt limit increase for free.

The statutory ceiling on the U.S. debt, according to GOP lawmakers, staff and conservative interest groups, remains their strongest leverage in getting the president to come to the table with deeper spending cuts — now and in the future. And Obama, in his opening offer in fiscal cliff negotiations, proposed eliminating the need for Congress to affirmatively raise the ceiling, arguing politics should not affect whether the U.S. government meets its obligations.

But since the president made that offer, Republicans have dug in on the issue, becoming almost preoccupied by their need to preserve that point of leverage during Obama’s second term.

“It’s all our guys want to talk about,” one senior Senate Republican aide said. The aide noted that Democrats should not misjudge the GOP’s willingness to hold the debt limit hostage and that the party will be in no mood to compromise on the issue if Obama keeps insisting on a massive tax increase.

Sen. Rob Portman, former director of the Office of Management and Budget, defended using the debt limit as a legitimate tool to extract fiscal changes. The Ohio Republican said that’s the only thing that’s worked in recent decades to bring deficits under control — though he acknowledged it caused disruption in 2011. Portman appealed to Obama to come to the table, noting that the rest of his agenda — from immigration to spending ideas — will rely on having a working relationship with the GOP.