WASHINGTON — As Speaker Nancy Pelosi solemnly declared the opening of a formal impeachment inquiry against President Trump last week, and the steady stream of Democrats supporting it became something of a stampede, a small group of Democrats remained unconvinced.

The cluster of skeptics, mostly moderate first-term lawmakers in conservative-leaning districts had dwindled to just a dozen by Friday, as lawmakers raced down the Capitol steps to catch flights and start two weeks of work in their districts. By then, many Democrats had joined the chorus of those backing an impeachment inquiry, worried about threats in primary elections and bowing to a rapidly shifting consensus in the caucus.

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But for a few determined holdouts, there is not yet a reason to endorse the inquiry.

Instead, those willing to elaborate on their thinking have called for a “fact-finding investigation,” urging their colleagues to take a more methodical approach that could rise above the partisan fray. They took care to stress that they were concerned about the allegations the president faced about his dealings with Ukraine.