WASHINGTON—President Barack Obama made an impassioned plea Friday to House Democrats in an 11th-hour bid to shore up support for his trade agenda ahead of a series of crucial votes.

In a rare visit to Capitol Hill, Mr. Obama delivered his closing argument to a Democratic caucus sharply divided over whether to support legislation that would grant the president fast-track authority for a Pacific trade deal—and extend aid to U.S. workers who lose their jobs because of foreign trade.

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