Three months ago, Democratic Party leaders took a stand: Fox News, President Trump’s favorite channel, and a reliable soapbox for attacks on liberals, was barred from participating in the party’s 2020 presidential debates. The move would ice out the network derided by critics as “state TV” from influencing the outcome of the Democratic primary.

Things have not exactly gone to plan.

By Sunday, the centrality of the Rupert Murdoch-controlled network to the party’s presidential contest was all but assured, as Senator Kirsten Gillibrand of New York became the fourth Democratic contender to sit for a Fox News town hall.

[On Fox News, Kirsten Gillibrand Talks Abortion, Al Franken and More]

Julián Castro, the former housing secretary, goes on Fox News next week. Pete Buttigieg, the South Bend, Ind., mayor, earned a standing ovation (and a presidential put-down) for his Fox News town hall last month. And candidates with dismal poll numbers are taking steps to woo the network’s bookers, viewing Fox News appearances — which tend to rate higher than town halls on rivals CNN and MSNBC — as an efficient and buzz-making path to raise their profiles.

Aides to Mayor Bill de Blasio of New York City, who scorched the Murdochs last year for “creating hatred and negativity and changing our political landscape for the worse,” recently approached the network. “We want to talk to all voters about why the mayor is the best candidate for working people — regardless of what news channel they watch,” a de Blasio spokeswoman, Olivia Lapeyrolerie, said on Sunday.