WASHINGTON—More Democrats from competitive House districts are getting behind their party’s effort to impeach President Trump ahead of a planned vote this week, despite some fears that their position could put their seats at risk.

The House plans to vote on Wednesday. With Mr. Trump’s impeachment looking likely, Democratic leaders were also set to announce as early as Monday which members had been suggested as impeachment managers—essentially prosecutors—during the Senate trial, which is expected to kick off in January.

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