“Twitter is the ultimate real-time engagement mechanism, so it’s moved everything to a much faster speed,” said Zac Moffatt, the digital director for the Romney campaign. “You have no choice but to be actively engaging it at all times.”

Mr. Romney’s aides say they can get a sense of where a story is headed before it is published simply by reading reporters’ Twitter messages. If reporters have flagged a particular incident on Twitter — for instance, the woman who stood up at South Carolina event and asked Mr. Romney, a Mormon, if he believed “in the divine saving grace of Jesus Christ” — Mr. Romney’s aides might pull him aside before a press conference and warn him that the topic is likely to come up.