Speaker Nancy Pelosi is resisting pressure from the Trump administration to quickly approve an updated North American trade deal and is telling lawmakers and union officials that a planned study of the agreement could drag on well into the fall, people familiar with the situation said.

Canadian Prime Minister Justin Trudeau introduced legislation in parliament on Wednesday to ratify the United States-Mexico-Canada Agreement, or U.S.M.C.A., and Vice President Mike Pence plans to be in Ottawa on Thursday.

But Ms. Pelosi’s escalating fight with President Trump, which erupted last week over the issue of impeachment, has soured many Democrats on doing anything that could possibly help the president. The war of words culminated with Mr. Trump calling Ms. Pelosi “Crazy Nancy” and “a mess” for lacking the intellect to comprehend the trade deal.

Ms. Pelosi has said privately that she is convinced the agreement can be approved — “I can get to yes” she told a supportive lawmaker last week — even if that would hand Mr. Trump with a much-needed domestic policy achievement ahead of his re-election campaign. But the president’s slight, in that it was a factor at all, only reinforced Ms. Pelosi’s resolve to extract significant revisions to the accord as a precondition of holding a floor vote, and those changes could require a renegotiation of the updated North American Free Trade Agreement, which the three countries agreed to last year.