Chris Christie, the Republican governor of New Jersey, put a second and final stop on Wednesday morning to the most expensive public works project under way in the country, a proposed rail tunnel under the Hudson River that could have doubled commuter-train service to Manhattan.

Mr. Christie had canceled the project earlier this month, saying that New Jersey could not afford its rising share of the projected costs. Then, pressed by federal officials to reconsider, he agreed to wait two weeks while alternative financing plans could be drawn up.

But, in the end, Mr. Christie said the taxpayers of New Jersey would still be liable for cost overruns that could run into the billions of dollars.

The decision to stop construction of the project, known as Access to the Region’s Core, could cost the state $3 billion that was pledged by the federal Department of Transportation for new transit projects, and some or all of an additional $3 billion commitment from the Port Authority of New York and New Jersey. The state was responsible for the balance of the project’s total cost, which had been estimated at $8.7 billion.

But Mr. Christie challenged that figure, saying the project would surely cost much more. Last week, the federal transportation secretary, Ray LaHood, who had tried to talk Mr. Christie out of stopping the project, said that his staff estimated that it would cost at least $9.775 billion and possibly more than $12 billion.