ESPN, under intense pressure again in the hypercharged terrain of social media, elicited a rebuke from a White House official on Wednesday in response to a series of Tweets posted by a “SportsCenter” host.

Jemele Hill, who co-hosts the 6 p.m. “SportsCenter” program, called President Trump a white supremacist on Twitter on Monday, adding: “Trump is the most ignorant, offensive president of my lifetime. His rise is a direct result of white supremacy. Period.”

Sarah Huckabee Sanders, the White House press secretary, said the comments were a “fireable offense.”

“I think that’s one of the more outrageous comments that anyone can make,” Sanders said Wednesday during a press briefing, “and certainly something that I think is a fireable offense by ESPN.”

ESPN, which like many news organizations has long wrestled with how to police employees’ social-media comments, said in a statement Tuesday afternoon that Hill’s comments “do not represent the position of ESPN.”

“We have addressed this with Jemele and she recognizes her actions were inappropriate.”

The reaction to Hill’s comments quickly escalated far beyond a debate over workplace protocols for social media. ESPN, increasingly criticized by conservatives for what they see as liberal editorializing, was suddenly a lightning rod in a political clash. The issue was explored on two prominent programs on Fox News, “Tucker Carlson Tonight” and “Fox & Friends.”

In May, after the company laid off about 100 employees, some conservative commentators claimed that ESPN’s financial position was declining because it had adopted a liberal slant. In August, ESPN pulled an announcer named Robert Lee from broadcasting a University of Virginia football game in Charlottesville, just days after a protest by white supremacists over the removal of a statue of the Confederate general Robert E. Lee. Again, conservative critics framed the episode as political correctness run amok.

The network has reoriented its programming more toward opinion and debate, encouraging some hosts to veer away from sports. Hill’s “SportsCenter” often mixes sports with social and cultural topics. Hill, who is black, and her co-host, Michael Smith, who is also black, frequently discuss black culture — uncommon for an ESPN show.

ESPN is hardly without conservative representation. Hill’s tweets were posted about an hour before the second broadcast of ESPN’s “Monday Night Football” doubleheader. The analyst for that game was Rex Ryan, who introduced President Trump at a rally last year. The show’s anthem was sung by Hank Williams Jr., a conservative who was once dropped by ESPN for comparing President Obama to Hitler.

Hill told The Ringer that she believes there is a portion of ESPN viewership that wants to see the faces on the network to remain mostly white. “As a discredit to all of us, they use words like too ‘liberal’ or too ‘politically correct,’ ” she said. “As if there’s ever been this widespread movement in television to just give black people and women shows. No, it’s been the exact opposite.”

ESPN has struggled to find a line for determining what is considered inappropriate commentary from its writers and TV personalities. Most prominently, Bill Simmons was disciplined three times, the last of which when he was suspended for three weeks without pay in 2014 after calling Roger Goodell, the N.F.L. commissioner, a liar on a podcast.

Hill was suspended for a week in 2008 after writing in a column that “rooting for the Celtics is like saying Hitler was a victim.”

In April, ESPN updated its “Political and Social Issues” guidelines to allow employees wider latitude in talking about politics when they intersected with sports. Political topics discussed should be “related to a current issue impacting sports,” according to the guidelines, and employees should “avoid personal attacks and inflammatory rhetoric.”