As for wooing centrists, keep in mind that Santorum was relatively successful at executing a kind of pincer movement in which he won some blue-collar voters to Romney’s left (not all of whom were Democrats trying to sow havoc in the G.O.P.) as well many voters to Romney’s right. The Sarah Palin who governed Alaska as an independent-minded populist might have executed the same maneuver even more effectively. But would the Sarah Palin who’s been branded as the Most Polarizing Woman in America have had the same capacity to win over independent voters in the Midwest? (Do we really think, as a for instance, that she would have outperformed Santorum among Catholics, the obvious place where he underperformed his?) There was a period when pundits were speculating, wrongly but not totally implausibly, that Santorum might have a better chance in the general election than Mitt Romney. Would anyone have argued the same about Palin, given her persistently upside-down approval ratings and the fact that the public’s perceptions of her seem so locked-in and unlikely to change?

The best reason to think that Palin would have given Romney a much longer and tougher fight than Santorum is that she would have polled in the double-digits from the beginning and might have consolidated the not-Romney vote early, by winning Iowa and South Carolina and clearing figures like Gingrich off the decks. But I still have trouble seeing which of the various crucial states Santorum lost to Romney that Palin would have won. Michigan? Ohio? Illinois? It’s certainly possible that she would rediscovered her Alaskan touch, and extended the campaign beyond what Santorum managed or even somehow won it. But I suspect that her trajectory might have looked more like Gingrich’s — some time at the top of the polls, a big win here or there that led the press to briefly anoint her the frontrunner, but then a swift drop-off once the Republican electorate focused on her general election liabilities.