House Republicans are rejecting a compromise offer from Democrats that would cut in half their proposed $22 billion increase to President Bush’s budget, but it’s unclear how long GOP leaders will be able to keep getting their Members to walk the plank against popular spending bills.

House Republicans barely found the votes to sustain President Bush’s veto of the Labor, Health and Human Services, Education and related agencies spending bill last week, and Democrats think they will either get a deal or be able to paint Republicans as heartless toadies of an intransigent and unpopular president.

Although Republicans have made the spending veto battle the key to restoring their tattered “brand” as the party of fiscal responsibility, and some conservatives dream of forcing Democrats to adopt a yearlong continuing resolution that would freeze spending across the board, others may be inclined to declare victory at a 50-50 draw rather than being forced to vote for ever-deeper cuts to domestic spending programs like home-heating assistance, cancer research and local aid as the holidays approach.

Shortly before the Labor-HHS override vote, House Appropriations Chairman David Obey (D-Wis.) laid out a litany of programs that would face the chopping block even with an $11 billion hike. Democrats say that such an increase would not keep pace with inflation for domestic programs.

Republicans, particularly in the Senate, have been quietly urging the White House to come to the negotiating table, but House Republican leaders and the party’s fiscal conservative wing have been hanging tough, at least rhetorically.

House Minority Whip Roy Blunt (R-Mo.) rejected the Democratic offer out of hand last week and said that Democrats need to negotiate with Republicans, not just the White House.

“At the end of the day, the White House doesn’t have to vote down here,” Blunt said. He later issued a stern press release criticizing the lack of specifics about which programs would get funded. “I do not support spending the hard-earned money of American families just for the sake of spending it. Yet, that is exactly what the majority is proposing. … House Republicans will not agree to waste more of the American people’s money just to say we ‘compromised’ with the Democrats.”

Brian Kennedy, spokesman for House Minority Leader John Boehner (R-Ohio), also sniped at Democrats:

“Aren’t these the same people who promised to deliver fiscal discipline to Washington? I don’t see a lot of discipline in fighting for more instead of less. House Republicans intend to hold the line with the President.”

But whether that Republican bluster will survive beyond Thanksgiving remains an open question. Supporters of spending programs are campaigning across the country to pressure Republicans, and the loss of even a few defectors would enable Democrats to override the president.

The stakes are high, not just in dollars but in showing whether Republicans can remain the same legislative force as Bush’s veto backstop heading into the 2008 elections as they have in 2007.

“This is about maintaining our relevancy,” said a House GOP aide.

But a House Democratic leadership aide dismissed Blunt’s comments. “I don’t know that he’s really important or relevant,” the aide said. “They’ve made it pretty clear they are a Bush rubber stamp, so if we get a deal with the White House, they’ll follow suit.”

The aide said Democrats are offering the compromise also as part of a message strategy to convince voters that they are willing to work across party lines but Republicans are not.

Rep. Rahm Emanuel (Ill.), chairman of the Democratic Caucus, ripped the Republican strategy as fundamentally flawed, pointing to the mountain of debt and war costs amassed under Bush.

“Do you think the American public forgot $4 trillion [in debt]?” he asked. “Do you think they forgot that his $200 billion for Iraq … is sitting over here?”

Republicans also face the prospect that if Democrats are ultimately forced to pass spending bills at the president’s numbers, earmarks will almost certainly get axed in whole or in part.

Despite much rhetoric by Republicans about cracking down on earmarks, behind the scenes most continue to fight for them as hard as ever and enjoy 40 percent of the earmarks in the bills. And while they might score political points if domestic earmarks are nuked for a second straight year — Democrats omitted them from the fiscal 2007 continuing resolution earlier this year — earmarks often are the only thing tangible that a Member in the minority can point to as bringing home to his or her district.

Republicans, meanwhile, have talked very little about domestic spending, with the exception of cutting earmarks, except in the abstract. They instead have focused much of their attention on Democrats’ failure to enact a veterans’ spending bill. But Democrats point out that they already have included every dollar that Bush sought for veterans as part of the continuing resolution, and are holding back an extra $4 billion or so because the administration has warned it will try to force Democrats to cut domestic spending to pay for the increase.

Emily Pierce contributed to this report.