“We are already hearing reports from unemployment officials from around the country that it will likely take weeks to stand up a new program and disburse benefits to these newly eligible workers,” Senator Mark Warner, a Virginia Democrat, wrote to Labor Secretary Eugene Scalia last week.

Mr. Warner urged the department to create tools, like a common online claims-processing system, so that states didn’t have to create their own infrastructure.

Critics also fear that the department may be excluding workers who should be able to receive the new benefit, citing guidance on eligibility that the department issued over the weekend.

“I’m deeply concerned that the Trump administration’s guidance to states on administering expanded unemployment insurance weakens the program,” Senator Ron Wyden, an Oregon Democrat, said in a statement on Monday. “It’s critical that workers who are unemployed through no fault of their own don’t fall through the cracks. Congress intended for these workers to be covered.”

In its guidance, the department appeared to leave out gig workers who could theoretically choose to work on any given day but have decided not to bother because so few passengers are requesting rides. It also appeared to exclude certain workers — such as older ones — who choose not to work because they are at a high risk of suffering serious health complications or dying from the coronavirus, although it indicated that those with compromised immune systems would be eligible.

And while the guidance allows the self-employed to claim benefits if they are unable to work because of child care needs while schools are closed, it implies that the benefits could expire once the school year ends.