But the federal Department of Transportation, which under President Trump was headed by Elaine Chao, did not respond to the application, despite repeated entreaties from Mr. Coscia and elected officials from New York and New Jersey. That stonewalling was the second major setback to a plan that dates back to the 20th century.
In a previous incarnation, the concept was known as the A.R.C. tunnel and it was going to lead not to Penn Station, but to a new terminal deep beneath 34th Street, near Macy’s flagship store. Construction had begun on that tunnel, with federal backing, when New Jersey’s former governor, Chris Christie, ordered a halt.
Mr. Christie, a Republican, argued that New Jersey would have been responsible for any cost overruns, which could have amounted to an unfair and unaffordable burden to the state. Democratic leaders from both sides of the Hudson were furious that Mr. Christie had passed up billions of dollars of federal money that would have flowed to the region.
Senator Chuck Schumer of New York, who is now the majority leader, was among them. From the start, Mr. Schumer has been an ardent champion of building a modern rail link to New York City. He pressed the Trump administration for approvals and funding, to no avail.
Now, with an ally in the White House, Mr. Schumer promised he will shepherd the Gateway program toward completion. Altogether, Gateway involves expanding Penn Station and adding tracks beneath it, as well as making improvements along the Northeast rail corridor, including replacing a 111-year-old swing bridge in New Jersey.
Mr. Christie’s successor, Philip D. Murphy, a Democrat, has staunchly supported the Gateway plan. His counterpart in New York, Andrew M. Cuomo, has at times raised doubts about his commitment to the tunnel project while he has focused on redeveloping the blocks around Penn Station.
But Mr. Cohen, a close ally of Mr. Cuomo, said on Friday that the governor would stick with the formula that calls for each state to cover 25 percent of the costs. He said Mr. Cuomo, “made it clear that whether he thought it was a good deal or not, he was not going to trade on that.”