House Republicans will "dig in" to ensure the extension of all expiring tax cuts, a GOP leader said Thursday.

Rep. Mike Pence (Ind.), the outgoing chairman of the House Republican Conference, suggested that the resurgent House GOP wouldn't be interested in any compromise President Obama might offer on extending the Bush tax cuts, which expire at the end of the year.

"There should be no higher priority than making sure that no American sees a tax increase in January. Not one," Pence said Thursday on WIBC radio in Indiana. "Republicans are going to dig in on that principle, and we're not going to go quietly if they take this last-minute lame-duck session as an opportunity to pile pork barrel spending and more deficit spending on the backs of future generations of Americans."

Obama and congressional Democrats had demanded earlier this fall, before the elections, that the tax cuts for households earning over $250,000 per year and individuals making over $200,000 be allowed to expire. Democrats wanted to extend all the other tax cuts. Republicans had demanded that all the expiring tax cuts be extended.

But Obama might be forced to come to the bargaining table, and the White House has suggested he might be open to doing so.

"We're certainly open to listening to their position, talking about it, and working together to find a compromise that moves this issue forward," White House press secretary Robert Gibbs said Thursday, weeks after the administration had sent clear signals that extending the high-end cuts was a non-starter.

Pence said that he had heard the White House was perhaps mulling "some sort of a deal" on the tax cuts, which prompted his declaration of disinterest on any such compromise.