Most New Jersey Republicans have remained publicly supportive of the governor throughout the ordeal of the long investigation. But there have been scattered signs that Mr. Christie’s once-firm grip on the state Republican establishment may have slipped along with his approval ratings.

As Mr. Christie has publicly entertained the notion of a run for the presidency, several prominent New Jersey Republicans once aligned with the governor have instead supported Jeb Bush, the former governor of Florida. Among them are Woody Johnson, the owner of the Jets, and State Senator Joe Kyrillos, the party’s 2012 nominee for the United States Senate.

Mr. Kyrillos, once one of Mr. Christie’s most enthusiastic supporters, also broke with convention when he publicly rebuked the governor last winter for mismanagement at the Port Authority of New York and New Jersey.

Despite periods of intense personal popularity, Mr. Christie has had only limited success at lifting the prospects of other Republicans. In 2013, the party made a major push to win control of the State Senate, hoping to ride Mr. Christie’s political coattails as he romped to re-election. Though he won a second term by more than 20 percentage points, Republicans failed to pick up a single seat in the chamber.

Still, the sheer breadth of Mr. Christie’s victories appeared to hold out the possibility of a larger political shift. In 2009, he won his first election by a wider margin than any Republican since Thomas H. Kean’s landslide re-election a quarter-century earlier.

National Republicans, reeling after their defeat in the 2012 elections, looked to Mr. Christie as a model for expanding the party’s electoral reach. Indeed, in his re-election campaign, Mr. Christie did the seemingly impossible, for a Republican: He won a clear majority of female and Hispanic voters, and split the youth vote almost evenly with his Democratic challenger, Barbara Buono, a state senator.

In his victory speech, Mr. Christie embraced the role, urging his fellow Republicans to campaign “in the places where we’re uncomfortable,” to court voters traditionally wary of conservative candidates.