David Samson, a longtime friend of Gov. Chris Christie, pleaded guilty to a felony count of bribery on Thursday and admitted that he had pressured United Airlines to operate a weekly flight to South Carolina for his personal convenience.

The plea, which was offered before Judge Jose L. Linares of United States District Court in Newark, appears to put an end to Mr. Samson’s career as a public official and power broker. And it casts a shadow over the political fortunes of Mr. Christie, a New Jersey Republican who until this week had been considered a potential running mate for Donald J. Trump, the party’s presumptive nominee for president.

“One of the problems with Chris Christie is there are skeletons in his closet that still have skin on the bones,” Patrick Murray, director of the Monmouth University Polling Institute, said.

The prosecution of Mr. Samson grew out of a federal investigation into the closing of access lanes to the George Washington Bridge in 2013. Federal prosecutors contend that allies of Mr. Christie at the Port Authority of New York and New Jersey conspired to tie up traffic on the New Jersey side of the bridge to punish a local mayor for declining to endorse Mr. Christie’s bid for re-election as governor.