PHILADELPHIA — Moments after the special counsel, Robert S. Mueller III, wrapped up his appearance at the Justice Department on Wednesday, Representative Dwight Evans stepped out of his district office in a black working-class neighborhood here to visit with local business owners. They had one question on their minds: Why is President Trump still in office?

Mr. Evans, a Democrat who began calling for Mr. Trump to be impeached long before Mr. Mueller issued his report, was not surprised: “The issue that I hear constantly here is, ‘We sent you for one reason only: to get rid of the president, right? Why haven’t you gotten rid of him yet?’”

In cities around the country, black Democrats like Mr. Evans — and other House members who represent majority-black districts — are hearing much the same from their African-American constituents, as well as from white liberals who have moved into the nation’s urban core. Those views are translating into action on Capitol Hill, where Speaker Nancy Pelosi is under increasing pressure from her rank-and-file to hurry up her time frame for what many see as an inevitable impeachment inquiry.

A number of prominent African-American lawmakers, including Representative Maxine Waters of California, the powerful chairwoman of the House Financial Services Committee, are leading the charge to impeach the president. On Wednesday, after Mr. Mueller declined to clear Mr. Trump, three more signed on: Representatives Bennie Thompson of Mississippi, who is chairman of the Homeland Security Committee, and Danny K. Davis and Bobby L. Rush of Illinois. All are veteran Democrats.