Specifically, many Republicans — including some of his supporters and donors — said Tuesday that Mr. Bush must finish ahead of Mr. Rubio in the primary here on Tuesday to justify continuing his campaign into South Carolina.

“If Rubio beats him badly in New Hampshire, Jeb is toast,” said Senator Lindsey Graham, Republican of South Carolina, a Bush backer who spent most of Tuesday traveling the state with him. Mr. Graham added that Mr. Bush must either “tie Rubio or beat him” in this state…

The prospect of the super PAC continuing its assault on Mr. Rubio after the New Hampshire primary leaves many Republicans uneasy about Mr. Bush’s intentions. And Mr. Rubio’s supporters, cognizant of these concerns, began moving on Tuesday to stoke these fears.

“If Jeb doesn’t do well there, and he’s still got millions and millions to spend, does he stay around?” mused Senator Cory Gardner of Colorado, a Rubio backer. “Who knows.”