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"But headed out the door to where? Oblivion?"

No.
There are three possible destinations:

(1) Headed home. Politics having become so mired in cronyism that key issues aren't addressed by either party, getting one's panties in a bunch over things political is a waste of time. Devote that time formerly devoted to politics to family and business pursuits. Pro-lifers in particular are likely to go home and drop out of politics if they become too disappointed with it. Most of them are family-and-church oriented, not rich enough for the tax breaks to make much difference, and only became interested in politics because of the pro-life issue. For them, the Supreme Court is the Holy Grail issue. Lose them, and they are simply lost to the political process. They don't switch parties. They just go home and don't come back. And their support is completely irreplaceable.

(2) Headed over to a protest candidate.
Ross Perot deprived Bush 41 and the Republicans of office, by giving angry and frustrated people on the right somebody to vote for. A vote for Perot and Admiral Stockdale was not necessarily a vote FOR Perot (at a certain point it became clear that the man wasn't quite "right"), but it was a jab in the eye of the GOP. A devastating one, in fact.
The nightmare candidate for the GOP in 2008 would be a retired US Army or Marine Corps general with solid wartime credentials who stands up and campaigns on third party national security: closed borders at home, and properly fighting the war in Iraq. Lots of people would vote for him: veterans, anti-immgration folks, and folks who walked out the door this time. Particularly in the Midwest, populist third party candidates build up a great mass like a summer squall line, because the Midwest is the least represented region by any electorate. The last election was decided in the Midwest, and the next one will be too, because every other region is sewn up by one party or the other.

(3) Headed into a Republican tent across the street to plan a coup. About a third of the party, roughly, including all of the most eloquent speakers, is incensed. They've built the party. They think that Bush is giving this pivotal seat to his crony. Bush is gone in 3 years. Right now, his loyalists dominate the party. But they don't control the microphones. The Limbaugh-Hannity-Coulter-Ingraham- Will wing of the party, the unhappy 1/3rd, control the microphone. Federalist society folks are pissed off right now too. They are a feeder for the Republican intelligentsia who AREN'T in charge right now.
The Bush loyalists, by trying to stiff-arm and tamp down the opposition in the Republican ranks here, are likely to create a civil war within the party, when the folks who head out the door for the moment, meet in a tent across the street and plot their return.

The better thing for Bush to do would be to withdraw this nomination and avoid this fight.

Some of the folks who head out the door will head out the door to political oblivion, and that will hurt the party net-net.
Others will head out the door for a Ross Perot type in the next Presidential election, if one presents himself. That will deliver a blow to the solar plexus.
And the third group will camp out across the street, and will not concede control of the Republican Party to the Bush loyalists, and start a long, nasty civil war within Republican ranks, which they will probably win, because the Bush's will be gone, and they've got no likely successor they can groom.