“Twitter has changed the whole way that politics works,” said Teddy Goff, the digital director of President Obama’s re-election campaign. “Not just the press element, but the organizing element and the fund-raising element and the relationship building that all campaigns try to do.”

Perhaps no Republican campaign monitors Twitter more closely than Mr. Romney’s operation, which believes that it can ferret out bias among reporters by analyzing their posts. Top aides say they watch Mr. Romney’s events with a Twitter stream open on their computer. Their war room compiles all the Twitter messages from the press corps at every event and e-mails them to the campaign staff.

“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.