But Mr. Christie’s star has faded as a potential vice-presidential pick. As polls show that his bluntness is striking more voters as bullying, Republicans close to Mr. Romney’s campaign say that the governor’s continued hostile encounters — including one on the Jersey Shore this month that was caught on video — have augmented fears that he is too unpredictable and too contentious, turning what was once viewed as a key strength into a drawback.

A decision to pass on Mr. Christie would highlight the more cautious approach Mr. Romney appears to be taking — by all indications he has been leaning toward measured personalities like Tim Pawlenty, the former Minnesota governor, or Senator Rob Portman of Ohio. This may reflect the lessons of the last presidential race, when a Republican running mate who seemed authentic and exciting went rogue.

But if Mr. Christie is not chosen, it would inevitably raise questions about his future in national politics, as it would with the other people who will soon find themselves on a list of almost-contenders.

Mr. Christie, 49, has made clear that not being selected as the vice-presidential nominee, after his public dalliance with running for the top spot on the ballot, would not be the end of his national ambitions — he has said that he thinks he will be a better candidate in 2016, suggesting that he thinks President Obama will win re-election.

But before then, he will need to balance his courtship of the national spotlight with the less glamorous realities of governing a state that is dogged by high unemployment, large revenue shortfalls and continuing political acrimony. And he must win re-election next year in conditions that are not as favorable to him as they were when he was elected in 2009. As many before him have discovered, a few extra years in office can remove a lot of the shine from a political star.