“It’s probably true that we appeal to white working-class voters,” said Brit Hume, the network’s Washington managing editor and the host of “Special Report.” “The candidates are going where the voters are.”

Conversely, Fox seems to have softened its stance toward the Democrats, mindful of the intense viewer interest in the prolonged primary season. Although Fox News remains firmly in first place among news channels, CNN has crept up in the ratings on primary nights. So Fox wants to appeal to people who might otherwise flip the channel in search of more time with the Democrats.

In short, Fox News and the Democrats abruptly find each other useful.

“I think the candidates are starting to realize that they need to reach the people who we reach already,” said Marty Ryan, the network’s executive producer for political programming.

Last year the Democrats declined most of the network’s interview requests. Barack Obama rejected the network for so long that the show “Fox News Sunday” resorted to a public demand in March, showing a weekly “Obama Watch” clock that counted the days since the senator had promised an interview and failed to make good.

Image Hillary Rodham Clinton and Bill OReilly on Fox. She has been on the network 10 times this year. Credit... Fox News

Then the thaw came. Mrs. Clinton has been on Fox 10 times this year, and Mr. Obama has appeared seven times, compared with three times for Mrs. Clinton and two times for Mr. Obama last year. Mr. Obama appeared on “Fox News Sunday” last week, perhaps in pursuit of moderate voters in Indiana and North Carolina.