NEW YORK — The “Bridgegate” scandal that rocked New Jersey Governor Chris Christie’s administration earlier this year is threatening a deal that would allow developer Larry Silverstein to finish building the next World Trade Center skyscraper.

Silverstein needs a guarantee from the Port Authority of New York and New Jersey to secure a $1.2 billion construction loan for 3 World Trade Center. On Wednesday, the agency’s board will vote on whether to approve that guarantee, part of a deal that would provide hundreds of millions of dollars more to the Port Authority and allow it to foreclose on the $2.4 billion tower if Silverstein cannot pay debt service costs.

But Silverstein’s deal, even with the concessions to the Port Authority, has become entangled in a fierce debate within the agency over its mission, including whether it should be in the real estate business at all.

Those questions have emerged since the so-called Bridgegate scandal erupted earlier this year. Operatives loyal to Christie’s administration caused massive traffic jams on the George Washington Bridge in September, an alleged act of political retribution against a local New Jersey mayor who did not endorse Christie for reelection.

The controversy has led to scrutiny of every corner of Port Authority operations, as well as the resignation of the agency’s deputy executive director and board chairman, both Christie appointees.

Critics have charged that rebuilding the World Trade Center area, which stalled for years after the September 11, 2001 terrorist attacks decimated the site, has taken too much time and energy away from other projects that are more critical to its bi-state transportation mission.

Silverstein has made progress on two of the other four planned towers at the site. The “Freedom Tower” at One World Trade Center is slated to open later this year, and the smaller 4 World Trade Center opened in November.

He has already spent about $500 million of insurance proceeds to build the lower eight floors of 3 World Trade Center under the 2010 agreement because some of the below-ground infrastructure there was needed to support a Port Authority transit hub.