Many public health experts, and some economists like Mr. Romer, say that a far more sweeping program would save lives and bolster the economy by helping as many Americans as possible learn quickly if they are infected — and then take steps to avoid spreading the virus.

Dr. Atlas and other administration officials playing influential roles in the government’s virus response effectively say the opposite: that more widespread testing would infringe on Americans’ privacy and hurt the economy, by keeping potentially infected workers who show no symptoms from reporting to their jobs.

Congressional Democrats have grown so frustrated with the administration’s testing efforts that as part of any agreement on a new aid package, they insisted on language that would force the government to carry out a far more prescriptive national program for administering and distributing tests.

While White House negotiators resisted those demands for months, Treasury Secretary Steven Mnuchin has said he will accept such wording with minor edits.