Then there is a broader concern that the symbiosis between Fox News stars and the Trump administration means the network will not treat Democrats fairly. On Monday, hours before Mr. Sanders went on the network, the chairman of the D.N.C. told a Fox News interviewer that he had no plans to reconsider his decision to bar the network from sponsoring an official party debate.
“I don’t have faith in your leadership at Fox News at the senior levels,” the chairman, Tom Perez, told the anchor Bill Hemmer.
Mr. Hemmer, who works on the reporting side of the network, pushed back, comparing Fox News’s opinion programming to that of a newspaper’s editorial page. “We’ll give you a fair shake,” he said.
That argument has been echoed by Fox News executives, who say that the Democrats’ debate decision was shortsighted and that the network’s reporters serve as neutral journalists. Mr. Wallace won praise in 2016 for his moderating of the third presidential debate.
Fox News declined to comment for this article.
Lesser-known candidates like Andrew Yang, a former tech executive, and Representative Tulsi Gabbard of Hawaii have made appearances in shorter segments on the network. But Mr. Sanders is currently a front-runner in the Democratic race, and his extended appearance Monday represented a bigger leap.
The audience on Monday was significantly larger than the 1.95 million who watched Ms. Harris on CNN in January, the previous benchmark for televised town halls. Mr. Sanders attracted more viewers between the ages of 25 and 54, the key demographic in cable news, than the same night’s broadcast of Rachel Maddow, who is MSNBC’s top-rated star.
Still, some candidates remain on the fence. And others seem ready to dodge the subject completely.
Asked on Tuesday if she would participate in a Fox News town hall, Senator Elizabeth Warren of Massachusetts told a reporter to speak to her communications director. “She’s the one figuring out where we’re going to go and who we’re talking to,” Ms. Warren said.
Contacted on Wednesday, the communications director, Kristen Orthman, declined to comment.