Republicans are mocking Democratic efforts to cast the partial government shutdown as a painful crisis created by President Trump. By deploying Mexican-inspired memes of Democrats including the House minority leader, Congressman Hakeem Jeffries of New York, the GOP is merrymaking to weaken the opposition’s narrative.

On Monday, when funding for non-essential government operations ran out, partisans on Capitol Hill traded blame. Republicans said that Senate Democrats voted against a continuing resolution because they wanted to fund health care to those in the country illegally; Democrats rejected the charge and cast Mr. Trump as the villain.

Mr. Trump ignored these and other thorny policy issues, instead launching a storyline more favorable to his goals. He did so with a video on Truth Social featuring Mr. Jefferies standing next to the Democratic minority leader in the upper chamber, Senator Chuck Schumer.

A sombrero had been placed on Mr. Jeffries along with a mustache in the style of a Mexican revolutionary, Emiliano Zapata, a symbol of rebellion and toughness south of the border. Mariachi music played while Mr. Schumer spoke, and similar parodies flooded social media in short order.

Ever since Mr. Trump entered politics, he’s displayed a knack for getting under the skin of opponents. The thought of ignoring him and staying on message is a discipline few have displayed. The standard reaction is to take offense and rally outrage.

“It’s a disgusting video,” Mr. Jeffries said on MSNBC, “and we’re going to continue to make clear bigotry will get you nowhere.” But the social media age thrives on juvenile humor and, as parents have long advised children, showing that teasing bothers you invites more taunting.

Mr. Trump, determined to dominate the Washington schoolyard, posted another video on Tuesday. In it, a mariachi band pops up behind Mr. Jeffries on MSNBC, the mustache and sombrero again in place. Mr. Trump is shown as the four musicians.

On Wednesday, the White House briefing room played the video “on a loop,” according to an independent journalist, Nick Sortor, on X. At the press conference that followed, Vice President JD Vance was asked if he thought the meme was “racist” as Mr. Jeffries alleged. “I don’t even know what that means,” he replied, adding that Mr. Trump was “joking, and we’re having a good time.”

ABC News put “AI-Generated Image” over the parody of Mr. Jeffries. CNN did the same. “It’s like,” Mr. Vance said of the notice, “do you really not realize the American people recognize that he did not actually come to the White House wearing a sombrero and a black, curly, animated mustache?”

If Democrats hope to make Republicans feel the heat, the White House is just as determined not to let anyone see it sweat. “You can negotiate in good faith,” Mr. Vance said, “while also poking a little bit of fun at some of the absurdities of the Democrats’ positions, and even poking some fun at the absurdity of the Democrats themselves.”

The Democrats tried joining the meme war, fighting on the ground Mr. Trump had chosen. on Wednesday on X, they posted a video of animated cats at the Capitol that began, “Kitty explains the government shutdown.” @GOP responded with a still of one of the cats with a sombrero and mustache.

On Wednesday, Senator Ted Cruz, a Hispanic Republican of Texas, got in on the act. “The 44 Senate Democrats who voted for Schumer’s Shutdown,” he tweeted, “should know that the sombrero posting will continue until they re-open our government. Hey, Macarena!”

The video with Mr. Cruz’s post featured mustachioed images of the Democratic senators accompanied by that 1993 hit, “Macarena,” by Los Del Rios. Late Wednesday, the White House X account reposted the first meme of Mr. Jeffries. “Every day Democrats keep the government shut down,” the message read, “the sombrero gets 10x bigger.”

In negotiations, it pays to strike a relaxed pose, and Democrats need the shutdown to sting if they’re to notch a victory. Every moment Republicans spend laughing shifts the narrative in their favor, indicating that the shutdown isn’t serious — and raising the odds that Mr. Trump will prevail just by throwing a sombrero in the ring.