WASHINGTON — As a former federal prosecutor, Representative Mikie Sherrill of New Jersey says she relies on evidence, and she needs to see more of it before considering whether to impeach President Trump.

Ditto for Representative Elissa Slotkin of Michigan, a former C.I.A. officer who has been studying the chapter on impeachment in a 1,068-page book on House procedures, and for Representative Lucy McBath of Georgia, who says she is “old enough to remember Watergate.” Representative Abigail Spanberger of Virginia swats away the question: “I’m focused on prescription drugs and infrastructure.”

In a House that can be dominated by loud voices on the left, these lawmakers — all freshman Democrats who flipped Republican seats in 2018 — form the backbone of a quiet power center, and centrist “majority makers” like Ms. Sherrill, Ms. Slotkin, Ms. McBath and Ms. Spanberger, all from districts won by Mr. Trump, will most likely have the final say on impeachment.

The president is testing their resolve on a near-daily basis. His declaration on Wednesday that he would take campaign help from a foreign power drew bipartisan condemnation on Capitol Hill and tipped a few more Democrats into the impeachment camp, but the majority makers stood firm. His blanket assertion of executive privilege over documents on the decision to add a citizenship question to the 2020 census strengthened the hands of Democrats who say the president’s stonewall of the House’s oversight function is, itself, impeachable.