The response seemed to defy the rough-and-tumble rules of modern politics. One of the nation’s most prominent opponents of same-sex marriage, Maggie Gallagher, had just told aides to Mitt Romney that she was endorsing Rick Santorum, a favorite of social conservatives, and encouraging her supporters to do the same.

So what did the Romney camp do? A few hours later, it invited her to send over a copy of her forthcoming book, for which Mr. Romney, it suggested, might provide a flattering blurb. “It was,” Ms. Gallagher recalled, “extremely unusual and gracious.”