Mr. Rubio, though, has a very different view of how the campaign is to be won. While he is stepping up his appearances in the early nominating states, his aides believe that garnering positive news coverage, especially in the widely viewed debates, is most crucial to early success, which then begets subsequent wins.

“Any venue we can create for Marco to communicate his message is a winner for us,” said Terry Sullivan, Mr. Rubio’s campaign manager. “More people in Iowa see Marco on ‘Fox and Friends’ than see Marco when he is in Iowa. Of course, that doesn’t mean you don’t go to Iowa.”

Mr. Rubio has drawn criticism in Iowa and New Hampshire for not showering more attention on those states, but his aides believe that primaries are increasingly nationalized, and they point to early-state and national polls showing the same candidates at the top.

They plainly believe in the need to stop Mr. Cruz. And that is a striking turnabout from October, when Mr. Rubio embarrassed Jeb Bush by saying in a debate that Mr. Bush was criticizing him because “someone has convinced you that attacking me is going to help you.” His own campaign, Mr. Rubio said, “would not be about attacking anyone else on this stage.”