“When the bomb dropped on us, what are you going to do? We never loaded them,” he said.

He said a number of area businesses would be affected, particularly shipping lines that focus on car exports. Mr. Spano said he did not think the entreaties of small business owners could influence the stalemate between New York and Washington. “It’s bigger than us, honey,” he said. “It’s bigger than us.”

Tim O’Day, the president of U.S. operations for Insurance Auto Auctions, a large company that is based near Chicago and processes more than 100,000 vehicles a year in New York, said the company has just recently started to assess the impact.

“We have learned that the policy change is limiting and halting our buyers’ ability to promptly export vehicles with New York ownership documents,” he said.

If the standoff continues, shipping lines specializing in exporting vehicles will probably reduce the number of calls to New York, focusing instead on ports in other states to meet demand for used cars overseas.

Mr. Cuomo, who had assailed the ban on Global Entry applications as “extortion,” met last week with Mr. Trump without reaching any deal. The New York attorney general has sued the federal government for what the office says is retaliatory action against the state.

A spokesman for U.S. Customs and Border Protection said in a statement that the agency checks vehicle identification numbers against state D.M.V. records to verify ownership and check for fraud. There has been a long history of theft rings exporting stolen cars from area ports.

“Because C.B.P. will no longer be able to carry out these checks against New York Department of Motor Vehicles records, the export of used vehicles titled and registered in New York may be significantly delayed,” the spokesman said.