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“TPA should come from the president’s leadership,” Mr. Kim said. “He has to say, ‘I need it for our economy.’ But he hasn’t done that. … [Mr. Obama] has to shore up support from his base of labor unions. So it’s very hard for him to be proactive and vocal about free trade.”

Mr. Obama is scheduled to travel to Asia in April, and administration officials are still hopeful that the free-trade deal can be reached in time for his trip.

“That would be an ideal time to wrap something up,” said Ms. Solis.