“Saturday Night Live,” too, has long put its male players in female drag, sometimes just for laughs and sometimes because it simply had too few female cast members to play all the necessary female roles. In 2013, Kenan Thompson announced he would no longer perform in a dress, tired of being the show’s go-to choice to play black female celebrities from Oprah Winfrey to Maya Angelou. The show subsequently hired two black female cast members, Sasheer Zamata and Leslie Jones. But it continues to put men in dresses — Fred Armisen’s character Regine, a mean, sexually demonstrative girlfriend, cropped up most recently in 2016.

As Mr. Spicer, meanwhile, Ms. McCarthy makes cross-dressing almost beside the point. She wears a fairly convincing wig, and her ill-fitting suit feels more like a joke about the poor tailoring that plagues the president and his administration than about the incongruity of a woman in male garb.

Ms. McCarthy isn’t funny as Mr. Spicer because she’s a woman, she’s funny as Mr. Spicer because she’s made a career of playing aggressive characters who are often angry for no reason. As Megan, in “Bridesmaids,” she broke new ground as a tough, crude woman with bizarre ideas and no boundaries who nonetheless finds romantic fulfillment, and in subsequent films like “The Heat,” she’s established herself as a powerful physical comedian whose best weapon is her snarl. On “S.N.L,” as she lifts up her podium to attack the press corps, it’s clear she was born to play the mouthpiece of an administration already defined by outbursts of rage.

While her gender isn’t the center of her performance, it matters. There’s a bit of an extra bite in a woman lampooning the spokesperson of a president who once bragged about grabbing women’s genitals, and who was reportedly moved to rage last month when attendance at women’s protests around the world dwarfed attendance at his inauguration. Add to that the fact that President Trump reportedly wants his female staffers to “dress like women,” and Melissa McCarthy dressing like a man to play his press secretary feels like a particularly astute way to needle the White House.