All 19 Democratic presidential candidates now support the impeachment inquiry, and many Democrats are optimistic that voters will as well, because Mr. Trump is so unpopular and the allegations against him are grave and easily grasped. For now, Republicans are the party on the defensive, flummoxed by the cascading disclosures about Mr. Trump that have threatened to upend his re-election campaign.

But there is also a general recognition, at every level of the Democratic Party, that impeachment could complicate their candidates’ efforts to explain their policy ideas to the country and persuade voters they have a vision beyond ousting Mr. Trump. The party has been disappointed too many times, its leaders say, by betting that Mr. Trump’s violations of political and cultural norms would bring about his downfall.

On Friday evening, Ms. Pelosi declared at a conference of New Jersey Democrats in Atlantic City that she would not allow the 2020 election to become a campaign about impeachment. Insisting the inquiry “has nothing to do with the election,” she said the campaign would be fought on other terms.

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“That’s about facts and the Constitution,” Ms. Pelosi said of the impeachment process. “The election is about all of the issues and policies that we have a difference of opinion with the Republicans on, and they are very drastic — and they have nothing to do with impeachment.”