Lawmakers of both parties, along with civil rights groups and state attorneys general, have raised concerns about the operational changes given the growing likelihood that many Americans will need to vote by mail this November because of the coronavirus pandemic. At a time when Mr. Trump is attacking mail-in voting, voting rights advocates fear that the slowdown in service could intentionally or incidentally undermine the integrity of the vote.Mr. DeJoy said on Tuesday that he would suspend some of the changes, but he has not committed to Democrats’ demands that he reverse some that are already in place, like the removal of hundreds of mail-sorting machines. Democrats are now trying to use Congress’s power to force him to do so and infuse $25 billion in emergency funding into the beleaguered agency, which has been rattled by the pandemic.Mr. Williams, one of the Republican-controlled board’s designated Democratic members, had served for 13 years as the Postal Service’s inspector general. A former Army intelligence officer, he had worked in similar watchdog roles at a handful of other agencies before that.Mr. Williams had not spoken publicly since he left the board of governors, but people familiar with his thinking have said he had grown increasingly alarmed about the politicization of the Postal Service and specifically the influence of the Treasury Department. Under Treasury Secretary Steven Mnuchin, a department task force has pushed for substantial cost-cutting changes at the Postal Service, which union leaders, Democrats and others contend are really an attempt to sabotage the agency to benefit private competitors.In their letter, Mr. Krishnamoorthi and Ms. Porter asked Mr. Barger, who has also donated to Republicans, to detail “any possible coordination you may have had with political entities when recommending Mr. Louis DeJoy to the selection committee.”The board of governors retained an outside firm, Russell Reynolds Associates, to help facilitate the search. But the lawmakers cite multiple unnamed people involved in the search saying that it was Mr. Barger, not the firm, who had injected Mr. DeJoy’s name into the process.In the interview with The Times, Mr. Barger said that the candidates were vigorously vetted and that Mr. DeJoy’s selection had been unanimous.Mr. DeJoy will testify before a Senate panel for the first time on Friday and before a House panel on Monday.Kenneth P. Vogel contributed reporting.