Senator John Thune, Republican of South Dakota, told reporters that Mr. Lighthizer had told lawmakers that the United States and Canada remained far apart on negotiations. “I’m not at all optimistic at the moment,” Mr. Thune said.

Senator Debbie Stabenow, Democrat of Michigan, said that it was possible for Canada to join the agreement with Mexico by November, even if the administration submits bilateral text to Congress this week. But any agreement, she said, “needs to be North America, to be the most effective.”

Congressional staff members cautioned that the administration would find little support on Capitol Hill for a deal that excluded Canada entirely, and that there was little appetite for pulling out of Nafta without a trilateral agreement to replace it. They also said that the agreement with Mexico alone would be unlikely to move to a vote in the House if Democrats win control of the chamber in November’s elections.

Senator John Cornyn, Republican of Texas, said that an agreement that excluded Canada would be much harder to pass in the Senate because it might not qualify for the trade protection authority provisions that would allow such a measure to be ratified with just 51 votes.

While some Senate Democrats agree with some of Mr. Trump’s goals on revising Nafta, they made clear on Thursday that they would punish him politically for excluding Canada.

“It would be a monumental mistake to do this without Canada,” said Senator Ron Wyden of Oregon, the top Democrat on the Finance Committee. “It’s basically surrendering on fixing Nafta.”

Representative Lloyd Doggett, Democrat of Texas, said that Mr. Lighthizer had told him that he would be releasing text of the agreement with Mexico this weekend and that he was hopeful that Canada would come on board after its provincial elections in early October. Mr. Doggett said he was not ready to say if he would reject an agreement with just Mexico, but said he had urged Mr. Lighthizer to keep working on the Canadians.