How will Republicans react to this in a broader sense?
The WSJ offered a tepid endorsement of Huntsman some time back. They'll no doubt credit's Obama's win to the weakness and belicosity of his challenger. The editorials might read something like "...with a nine percent unemployment rate and a 52 percent disapproval rating, President Obama should have been an easy target for the GOP, but the political suicide machine is a well-oiled and effective one, and the Republicans have used it yet again to ensure a GOP defeat. This is particularly unfortunate since the GOP will control both chambers of the congress and it might have meant our best chance to derail President Obama's legislative agenda, including the controversial medical care reform bill..."
Others, including 6 governors, 15 senators, and a boatload of house members, have endorsed Romney. They'll probably conclude that Romney would have made a better candidate. But most of them will have voted for Gingrich in the general election and can't be too harsh on him. Other influential republican sympathizers, such as the talking heads on Fox News that have endorsed Romney, will make similar arguments.
In the end, the rank-and-file republicans, those who don't hold offices or host talk shows but who voted in the primaries, will likely point to a combination of factors, including the weakness of the field that led them to nominate Gingrich, as well as a rebounding economy and the aptly-named Campaign Finance Reform Bill that so reformed campaign financing that it allows millions of unaccountable dollars to speak for and against candidates. They probably won't speak of Obama as a better candidate, even if that turns out to have been the case.