Lawmakers initially suggested that a Senate vote on the pact would be delayed until after the trial, which will begin in earnest on Tuesday and eat into the Senate’s time for legislative work. But when Speaker Nancy Pelosi of California decided to delay sending the articles of impeachment, senators seized the opportunity to move on the trade pact.

“Our farmers and ranchers expect us to move on this,” Senator Joni Ernst, Republican of Iowa and a prominent advocate for the deal’s passage, said at a news conference on Tuesday.

“Folks back home, they don’t care what’s going on in this bubble surrounding impeachment. They just simply want to know are we doing the work that’s important to them,” she said.

Within nine days, six Senate committees had given the implementing legislation seals of approval, allowing for the vote to occur Thursday morning before the impeachment trial formally began.

“Undaunted by those who set to throw him out of office since day one, President Trump forges ahead for the good of the American people,” Senator Charles E. Grassley, Republican of Iowa and chairman of the Senate Finance Committee, said. “Passage of U.S.M.C.A. is better late than never.”

The bipartisan support for the deal came at a moment when partisan politics have stymied most legislative efforts. In part because of the Democratic stamp on the pact’s terms, 37 Democrats joined 51 Republicans in voting for the deal, including opponents of the original North American Free Trade Agreement and others typically averse to trade pacts.

“I never thought I’d be voting for a trade agreement during my Senate tenure that I wrote a big part of,” said Senator Sherrod Brown, Democrat of Ohio, whose vote for the pact was his first for a trade agreement in a quarter century. Mr. Brown embraced the measure after labor enforcement language that he and Senator Ron Wyden, Democrat of Oregon, crafted was included in the final agreement.