Several White House officials expressed agreement during a senior staff meeting on Monday morning that the president’s attacks were a bad move, according to people informed about the discussion, but they were uncertain who could intervene with him — or if anyone would even dare try.

They privately scoffed at the idea that it was strategy rather than impulse, concluding that any political benefit he might derive by revving up his conservative, largely white base could be offset by alienating more moderate voters in the suburbs of states like Wisconsin and Michigan that he needs to win a second term.

Three advisers said the president complained about Mr. Cummings throughout the weekend. Two of those advisers said the real source of his ire was the decision by the House Oversight and Reform Committee, which Mr. Cummings leads, to authorize subpoenas for all work-related texts and emails sent or received by Mr. Kushner and Ivanka Trump, the president’s elder daughter and senior adviser, on personal accounts.