At the end of the long stare-down between the governor of New Jersey and federal officials over the money spent on tunnels that were never built, both sides blinked.

On Friday, Gov. Chris Christie and Ray LaHood, the federal transportation secretary, announced that New Jersey would pay back $95 million that the federal government had provided for a pair of rail tunnels under the Hudson River that were projected to cost $8.7 billion. The effort, known as Access to the Region’s Core, or ARC, was one of the biggest public-works projects under way in the country when Mr. Christie decided to cancel it one year ago.

Mr. Christie maintained that his state could not afford to shoulder potentially huge cost overruns on the project, which would have doubled the train capacity between New Jersey and New York City. His unilateral decision to scrap the tunnels enraged Senator Frank R. Lautenberg, who had spent years lining up $6 billion in commitments from the federal government and the Port Authority of New York and New Jersey.

Mr. LaHood, who was also angry at Mr. Christie, demanded that New Jersey repay all of the $271 million in federal money that had gone toward the early stages of building the tunnels. The governor responded by declaring, “We are not paying the money back.”