In recent days, however, the combination is emerging as something less obvious: an opportunity.
Recent polls have shown Bush's popularity -- which has long been in the tank with independents -- suffering significant erosion even among GOP base voters, largely due to a backlash over the president's stance on immigration.
The decline, according to some Republican strategists, has flashed a green light for lawmakers on Capitol Hill and presidential candidates to put distance between themselves and an unpopular president -- a politically essential maneuver for the 2008 general election that remained risky as long as Bush retained the sympathies of Republican stalwarts.
Now that those sympathies have somewhat cooled, the effects are visible: Republican House members upset about immigration policy have spoken of Bush in disparaging terms. And presidential contenders like Rudy Giuliani are striking change-the-course themes in their rhetoric, even while continuing to back Bush over the Iraq war.
The change, say GOP operatives, is the absence of fear about being perceived as something less than an ardent Bush backer. "What's the penalty now, Karl being mad at you?" Republican pollster Tony Fabrizio asked with a laugh, referring to Bush political adviser Karl Rove. "Who cares? Even his former chief strategist (Matthew Dowd) walked away from him and pissed all over him."
For candidates trying to woo right-leaning primary voters -- while also trying to show the broader electorate that they are not simply a rubber-stamp for Bush -- immigration has become a well-timed issue over which to break with an unpopular incumbent. "It presents the Republican presidential candidates with a helpful opportunity to separate themselves," said GOP consultant John Brabender. "It shows independence, that they're not in step with the current administration, and it plays toward conservative voters."
Two polls last week recorded a dip in Bush's standing with Republicans. In a Quinnipiac University poll, Bush's support among GOP voters fell to 61 percent, from 74 percent earlier this year. An NBC News/Wall Street Journal poll found the same thing, with Bush GOP support dropping from 75 percent in April to 62 percent now.
The trend, while still leaving Bush with clear majority support among Republican voters, is noteworthy because, for most of the past several years, Bush's hold on the GOP was solid even as he became one of the most unpopular presidents in history among Democrats and was running poorly among independents.
Now, Republican disapproval of Bush has increased from 20 percent in November 2006 to 31 percent this month, Quinnipiac polling demonstrates. Nearly half of all GOP moderates express disapproval with the president, including self-described "not strong" Republicans and independents who lean toward the GOP.
The approval of "not strong" Republicans has slid 16 percent in a half-year, where it stands at 44 percent. "Strong Republican" support has slid 9 percent over the same period, where it currently rests at 72 percent, the Quinnipiac poll conducted June 5-11 found. Both Quinnipiac and NBC/Journal put Bush's approval rating with all voters just under 30 percent.
Republican pollster Neil Newhouse, who conducted the NBC/Journal poll June 8-11 with Democratic pollster Peter Hart, said the poll showed no erosion in Bush's support over Iraq. That leads him to attribute the softening among Republicans mostly to the president's support for a proposed overhaul of immigration laws, including provisions that critics say are equivalent to amnesty for illegal immigrants.
Reverberations are already being felt in congressional races. In a special election Tuesday in the conservative 10th District of Georia to replace the late Rep. Charlie Norwood (R), Republican candidates have been under constant pressure to come out against the legislation and demand border security first, possibly through separate spending legislation. The race serves as a harbinger for the pressures Republicans may face from their right flank in the 2008 races.
At the most recent GOP debate, only Sen. John McCain (R-Ariz.) defended the legislation. Other GOP candidates were unified in their opposition to the proposal, which remains on legislative life support on Capitol Hill.
When Bush publicly criticized the motives of opponents of his immigration package, Minority Whip Roy Blunt (R-Mo.) called Bush's remarks "unhelpful and uncalled for." Rep. Ed Royce (R-Calif.) reportedly responded that Bush would "rather disparage the motives than look at the factual questions."
But the willingness of leading Republicans to draw distinctions with Bush goes beyond immigration. "The thing that concerns me the most is that 74 percent that thinks the country is headed in the wrong direction," Giuliani said last week at a Flag Day ceremony in Wilmington, Del., in a reference to recent polling. "What we're lacking is strong, aggressive, bold leadership like we had with Ronald Reagan." Later, he sought to downplay the apparent shot at the incumbent, underlining the awkward balance GOP candidates must strike in establishing independence from Bush without expressly repudiating him.
But some Republicans have lost patience with holding their tongues. The issue of immigration "is symbolic for a lot of Republicans of the crap that (Republicans) have had to swallow," said Fabrizio, who was a strategist for 1996 GOP nominee Bob Dole. He cited the No Child Left Behind education measure and an expensive Medicare prescription drug benefit.
Senior aides to McCain, Romney and Giuliani all sounded familiar tones in explaining how they would deal with the Bush burden. It's what Democratic politicians from Republican-leaning states would say about Bill Clinton in the 1990s and what Republican politicians from Democratic-leaning states say now about Bush: We'll agree with him where we agree him and disagree with him where we disagree with him. It's hardly a ringing endorsement, but even such tepid comments may not be sufficient to escape the Bush drag in 2008.
Brabender believes it's a matter of when -- not if -- the Republican hopefuls begin to more clearly ease away from the incumbent. "Personally, I don't think they have a choice," he added. "2006 was a referendum on the president, and we saw how that worked out. It would be a disaster to have the same question in 2008. …I don't want to call it an exorcism among the party, but at some point there needs to be a firewall put up where (the candidates) partition off the president."