Tuesday’s vote was the second time the Senate had blocked a filibuster of fast-track authority, but this time the bill was shorn of a separate measure to offer enhanced retraining and educational assistance to workers displaced by international trade accords. That measure also faces a crucial vote on Wednesday.

Passage of a stand-alone trade promotion bill will put pressure on House Democrats, who just over a week ago brought down the worker aid provision, known as trade adjustment assistance, when it was linked to the fast-track legislation, in a strategic move they hoped would defeat the entire trade package.

But Republican leaders — with support from the White House — found a parliamentary way to corner the Democratic opponents, by separating the two pieces of the bill. By Wednesday evening, legislation will most likely be on the president’s desk, giving him the power to complete the Trans-Pacific Partnership. He can sign it whether or not the House passes worker dislocation assistance when it is scheduled to come to a vote late Thursday.

Josh Earnest, the White House press secretary, said House Democrats should get on board.

“The previous explanation that we heard from some Democrats who voted against trade adjustment assistance — something that Democrats have steadfastly supported for decades — is that they were doing that in an effort to slow down the advancement of trade promotion authority legislation,” he said. “That will no longer be a factor to consider.”

The tortuous path of the trade legislation over the last six months created the unusual alliance between Mr. Obama and Republican leaders, who otherwise have worked to thwart him on domestic and foreign policies.

“Occasionally, even the leader of the Democratic Party, the president of the United States, gets things right,” said Senator John Cornyn of Texas, the No. 2 Republican.