Uh, not likely. Whatever you think of the legislative branch's involvement, it's doubtful the issue will be a political albatross for the GOP any more than, say, the Elian Gonzales scandal permanently tarnished the Democrats. Indeed, recall that the Clinton impeachment drive was far more deleterious for the GOP's standing in the polls over a far longer period of time, and if that effort did permanent damage to the Republican Party, it's hard to find today. The federal government is run by Republicans for as far as the eye can see.
True, the conservative coalition has its share of contradictions, but that's to be expected of any growing ideological movement or political party. Franklin Roosevelt's coalition included racist Southerners, progressive blacks and Jews, liberal reformers, grafters and machine bosses. These people fought a lot. They fought over policy, and they debated who really had Roosevelt's support. From the 1920s to the 1950s, a debate raged around the question, "Whither liberalism?" Was it over? When did it die? What does it mean now?
Something similar has been going on with conservatism ever since William F. Buckley launched National Review. From the 1950s onward, various conservatives - mostly, but not entirely, of a libertarian bent - have predicted the movement must come a cropper from its internal contradictions. Buckley was constantly fending off assaults from ideological brigands trying to commandeer the ship of conservatism and steer it toward purer waters of religious, libertarian or anti-Communist hues. Buckley stood firm and said, no! There be monsters there. Buckley was aided by the conservative theorist Frank Meyer, who fashioned the doctrine of "fusionism," which held that freedom and virtue were inextricably entwined; virtue not freely chosen is not virtuous.
As conservatism blossomed in the 1980s under Ronald Reagan, some conservatives jumped ship, unwilling to accept the compromises and responsibilities of power. The late "paleocon" Samuel Francis bemoaned the Reaganites as "hapless" sell-outs. Others among his confreres banged their spoons on their highchairs because "neocons" got jobs in the administration they felt were rightly theirs. On foreign policy, realists, neoconservatives and traditional anti-Communists tussled in an endless mosh pit.
In 1992, R. Emmett Tyrrell proclaimed that a great "conservative crack-up" was taking place before our eyes. Throughout the 1990s other conservatives made similar pronouncements, even as conservative ideas won under a Democratic president and Republican politicians inexorably claimed majority party status in this country.
Personally, I dislike much of Bush's "compassionate conservatism." Indeed, I find it astounding that even as Bush has moved the Republican agenda leftward in many key respects, the left has screamed all the louder about how "right wing" he is. But simply because I think Bush is wrong about, say, Medicare, it doesn't mean I think it's a sign the conservative movement is falling apart. Lots of folks thought FDR's New Deal was a disaster at the time, and look how that turned out.