Governors, who usually control their state party machinery, are always courted by presidential candidates, particularly in the states with the earliest contests, like Iowa and New Hampshire. But for contenders to make the pilgrimage to New Jersey — not a pivotal primary state — with aides in tow, for face-to-face sessions with a governor long before any votes are cast, is something else.

“There hasn’t been any parallel to this, not in my memory,” said David P. Redlawsk, a political science professor at Rutgers University. “He’s a hot commodity, and the candidates clearly think his endorsement would be significant. He can attract crowds and raise a lot of money. I wouldn’t be surprised if they’re thinking about him as a potential V.P. candidate.”…

The Iowans are the only Republican operatives to make an organized appeal to Mr. Christie, but informal inquiries are common, said William J. Palatucci, one of the governor’s closest confidants.

“I think a lot of people think that in private they’re going to get a wink or a nod, some kind of hint from me or DuHaime,” he said. “But the answer’s the same.”