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Mr. Perry and Mr. Walker are on the RGA’s executive committee, and Mr. Jindal is the current RGA vice chairman and therefore is eligible for another turn as chairman after his initial term last year. Mr. Jindal has said explicitly that Mr. Christie should stay on as chairman.

Many Republican strategists are focusing early in the election cycle on independents — the swing voters who swung away from the party as part of the 2008 and 2012 presidential losses. Mr. Christie remains one of the strongest Republicans among independent voters.

In the latest CNN survey of Republicans and independents, former Arkansas Gov. Mike Huckabee led the theoretical field with 14 percent, with Mr. Paul second at 13 percent and former Florida Gov. Jeb Bush and Mr. Christie tied at 10 percent each.

Although party operatives have an implicit obligation to speak well of troubled Republican politicians, such expressions of support are not much of a stretch in Mr. Christie’s situation.

Mr. Cox noted that Mr. Christie and his fellow Republican governors raised $6 million for the RGA war chest in January — after “Bridge-gate” broke. The New Jersey governor returned from a recent Texas swing with an impressive $1.5 million haul for the RGA.

Republicans agree that the only thing that could lead the RGA chairman to step down would be the surfacing of indisputable evidence that he knew before or during the four-day traffic tie-up on the George Washington Bridge that it was meant as political payback for the local Democratic mayor. Unlike other big-name Democrats in the state, the mayor refused to endorse Mr. Christie’s re-election in November.

One of his biggest selling points among Republicans looking for a winner in November 2016 is his demonstrated ability to attract independents and Democratic crossovers along with voters in his own party. Mr. Christie won a landslide re-election in November.

In theory, an RGA chairman has an advantage over potential rivals because he builds name recognition and collects political IOUs by traveling across the country to raise money for gubernatorial elections. Yet the number of governors who used the RGA chairmanship as a springboard to the presidency is few, but includes Ronald Reagan.