WASHINGTON — President Obama will give a rare interview on Wednesday to Fox News, the cable network that a top administration official once accused of being a political arm of the Republican Party.

The interview, with Bret Baier, an anchor and a former chief White House correspondent for Fox, will be broadcast at 6 p.m., at the height of a week in which Democrats, including Mr. Obama, are pressing allies and lawmakers to push ahead to get the health care bill passed in the House despite solid Republican opposition and the lessening of public support for the legislation.

At the briefing on Tuesday, Robert Gibbs, the White House press secretary, was asked if the president believed he could really change the minds of viewers who watch Fox. It is “certainly worth a shot,” Mr. Gibbs said, adding that Mr. Obama was well aware that wavering Democrats and their constituents tuned in to the network.

Last year, however, Obama administration aides used the in-house White House blog and other news media to criticize Fox for its coverage, particularly its commentary. Fox officials defended their reporters, taking pains to put distance between pundits and those working the White House and other beats.