But there is a potential impediment to the G.O.P. plan — the leader of the party himself.

Eager to continue trade talks, uneasy about further rattling the markets and hungry to protect his relationship with President Xi Jinping at a moment when the United States is relying on China’s manufacturers for lifesaving medical supplies, Mr. Trump has repeatedly muddied Republican efforts to fault China.

Even as the president tries to rebut criticism of his slow response to the outbreak by highlighting his January travel restrictions on China, he has repeatedly called Mr. Xi a friend and said “we are dealing in good faith” with the repressive government. He also dropped his periodic references to the disease as “the China virus” after a telephone call with Mr. Xi.

Yet in private, he has vented about the country. Senator Kevin Cramer of North Dakota said he informed Mr. Trump in a Thursday telephone conversation that the meat processing plant in South Dakota suffering a virus outbreak is owned by a Chinese conglomerate. The president responded, “I’m getting tired of China,” according to Mr. Cramer.