The sense that Mr. Rubio’s position has improved is reflected in the betting markets, which show him rising steadily to a 29 percent chance of winning the nomination, more than twice the 13 percent he held before the last Republican debate. Mr. Bush is at 31 percent.

Mr. Rubio, however, will still need to capitalize on the voids created by Mr. Walker’s exit and Mr. Bush’s weakness. With well-received debate performances, he has been praised as the best communicator in his party and has strong favorability ratings. But he has not yet become the top choice of many party elites or voters; in fact, he holds about as much support in the polls as Mr. Bush, and far fewer endorsements.

Mr. Rubio’s biggest shortcoming is that he is not the natural favorite of any wing of the party, which is the easiest way for a candidate to become the first choice of a meaningful block of voters. He’s the opposite of candidates like Mr. Cruz, Mike Huckabee, Rand Paul and John Kasich, who have messages and political identities that resonate with one of the party’s core constituencies, like the Tea Party, evangelicals, libertarians or moderates.

Mr. Rubio’s challenge could simply be a reflection of his greatest strength — his wide appeal.