But the problems he'll be leaving behind are not likely to go away soon. The Alito nomination fight is expected to extend into early next year.
Even if Bush wins and Alito is confirmed, it could be much more difficult to get action on the rest of his second-term agenda, including major cuts in spending and taxes. If he loses, the consequences would be even worse for the White House.
Armed with evidence from Alito's substantial record as a judge, activists at each end of the political spectrum are launching the long-expected public relations war over the future of the Supreme Court that largely fizzled during the Roberts and Miers nominations.
The result of their efforts, from the grassroots to the media airwaves, as well as Alito's testimony during his Senate hearings, could further alienate centrist voters, including the independent moderates highly prized by both parties.
A leading conservative activist, James Dobson of Focus on the Family, praised Alito, adding that "any nominee who so worries the radical left is worthy of serious consideration."
Tacit acknowledgment that Bush had helped himself politically could be glimpsed in Democratic Party Chairman Howard Dean's attack on what he termed the president's "capitulation" to the GOP's conservative wing."
"A lifetime appointment to the Supreme Court," Dean said in a statement, "is too important to be sacrificed on the altar of short-term political gain."
Perhaps more worrisome, from the Republican perspective, is the threat that in firing up his supporters, Bush will be galvanizing the opposition, too, possibly making it easier for Democrats to raise money around the Alito fight.
"I think it's going to be very energizing to the Democrats in a way that Roberts couldn't be," said Dunn, particularly on the issue of abortion. "We're not talking about chipping away at Roe v. Wade with this guy. We're talking about overturning Roe v. Wade."
With emotionally charged issues such as abortion and gun control expected to figure prominently in the confirmation debate, the Alito nomination has effectively signaled the start of the 2006 campaign, a midterm struggle in which continued Republican control of Congress will be at stake.