Beyond the president’s efforts to impede the special counsel’s investigation, Democrats also plan to scrutinize his role in hush payments to two women who said they had affairs with him and reports that he dangled pardons to officials willing to break the law to implement his immigration policies. Democrats also demanded documents last week related to whether his resort properties illegally profited from government business.

“The central oversight perspective so far has been focused on the Mueller report,” said Representative Jamie Raskin, Democrat of Maryland and a former constitutional law professor who sits on the Judiciary Committee. “We need to broaden out the oversight work to get a complete picture of the lawlessness of the administration. That is the imperative for the fall season.”…

But even the most ardent supporters of impeachment conceded that time might already be short, with only around 40 days in session left before the end of the year and a slew of issues on Capitol Hill that could sap additional time and energy. Congress must fund the government in the coming weeks, and lawmakers in both parties want meaningful legislative debates over Mr. Trump’s trade deal with Mexico and Canada, gun safety legislation and bolstering election security.

Most House Democrats now privately agree that Mr. Trump’s behavior clears the bar for an impeachment vote — some reached the conclusion over the six-week recess that just ended — but the politics of doing so are more complicated and their leaders appear no closer to a decision on whether to proceed.