At one point, Mr. Short directed Dr. Robert R. Redfield, the head of the Centers for Disease Control and Prevention, to soften the agency’s recommendations to a meat processing company about safety steps, in part to placate the embattled industry. Mr. Short was also part of a small group, which included Kellyanne Conway, then a senior adviser to Mr. Trump, that pushed to change C.D.C. guidance on church reopenings.

Interviews with task force members, government public health officials and current and former White House officials show how public health considerations were sometimes at odds in the task force with the White House’s imperative for 2020: winning re-election on the basis of a strong economy.

“The vice president admittedly was in a difficult situation; he was asked to lead a project where his boss wasn’t on board,” said Senator Angus King, independent of Maine, who clashed with Mr. Pence during an April conference call about coronavirus testing. During that call, Mr. King erupted at the vice president for what he believed were his evasive answers.

“And so, the question is: To what extent, if any, did he try to push back on the president, minimizing masks, minimizing testing, continually claiming the virus was behind us?” Mr. King said. “And it looks like he didn’t.”