And even as they ready an onslaught of investigations into alleged malfeasance by the president and his administration, they said common ground could be found with Mr. Trump.

“We’re still going to have Donald Trump as president, so obviously that’s going to limit to an extent what we can accomplish in the short term,” Representative Jim McGovern, the Massachusetts Democrat who would be in line to chair the Rules Committee, said in an interview. “But one thing we can accomplish is we can run the place like professionals and restore some integrity to the institution.”

Democrats, of course, may fall short of a majority on Tuesday, and if they do net the 23 seats they need, there is no guarantee Mr. Trump, or Republicans who are expected to maintain control of the Senate, will cooperate. Mr. Trump has shown an interest in working with Democrats in the past, on issues like gun control and immigration, only to backtrack, and he could emerge from Election Day determined to shun Democrats.

Senator Mitch McConnell of Kentucky, the majority leader, would have his own motivations to bypass or block House proposals as he blockaded legislation pushed by President Barack Obama. Then there is the challenge of reining in the most energized liberal lawmakers for whom anything short of a presidential impeachment would be a compromise too far.

But after eight years in the minority, most Democrats believe they will need to do more than embarrass the White House with subpoenas and investigative hearings if they want to be more than a one-term majority and reclaim the presidency in 2020. Ms. Pelosi made clear her party would only bend so far. Democrats are not “going to lowest common denominator to get a presidential signature,” she said.