But perhaps the biggest sensitivity involved Mr. Trump, who has sought to discredit the debate process from the beginning. Despite the fact that debates have been scheduled to compete with major sporting events in previous years — they always take place in the fall when the baseball and football seasons are in full swing — he claimed that the commission was deliberately scheduling them opposite N.F.L games so fewer people would watch.

Complicating matters further, Mr. Trump has a long and chilly relationship with one of the co-chairmen of the commission, Frank Fahrenkopf. In particular, Mr. Fahrenkopf and Mr. Trump butted heads over Mr. Trump’s unwillingness to pay dues to the association, said one person who knows both men.

For the candidates, the debates may be the best remaining opportunity for both candidates to reshape the 2016 race — and for Mr. Trump, who is trailing in the polls, to gain ground against Mrs. Clinton.

Debates have allowed challengers and relative political newcomers to reach out to reluctant voters, providing reassurance about their qualifications. Barack Obama and Bill Clinton helped put to rest questions about their preparedness for the presidency in confident debate exchanges. George W. Bush defied the caricature of himself as a lightweight by holding his own against Al Gore.

Mr. Trump, facing significant skepticism among voters about his character and temperament, will be aiming for a similarly forceful performance. But Mrs. Clinton is one of the most practiced debaters in modern politics, after two campaigns for the Senate and the presidency, and she is perceived to have a considerable advantage.

Mr. Wallace’s appointment was celebrated in a letter to employees from Rupert Murdoch, the media mogul overseeing Fox News, which was besieged this summer by the sexual harassment scandal involving Roger Ailes, who founded and led Fox News. But Univision, the Spanish language broadcaster, sent a letter to the commission protesting the absence of a Hispanic moderator, calling it “an abdication of your responsibility to represent and reflect one of the largest and most influential communities in the U.S.”

Presidential debates provide a prestigious stage for newscasters, especially in this tumultuous election season, which produced record television ratings for debates. The first Republican debate last August attracted 24 million viewers, the highest rated nonsports cable event in history. Democratic debates similarly broke viewing records for the party.