Walden continued: “And I think what the Democrats ran into with their caucus in Iowa, where they thought they had the whiz-bang program to count delegate votes, and we all saw the disaster out of that. And so I think this is a horrible time to suddenly mandate to our states, here’s how you’re going to run the next election. Oh, and by the way, you have just a couple of months to pull it off.”

As coronavirus cases soar past 400,000 in the U.S., with nearly 13,000 deaths, state elections have become a point of contention among lawmakers as some, mostly Democrats, argue that in-person voting at polling places is anathema to the social distancing guidelines issued by the federal government. Earlier this week, Democratic Wisconsin Gov. Tony Evers pushed to postpone the state’s April 7 election, an effort that was blocked by the Wisconsin Supreme Court, prompting long lines of face-masked voters queueing up at a drastically reduced number of polling places.

While Walden's criticism of a national mail-in voting program was largely logistical, President Donald Trump has claimed the practice is "corrupt" and that “a lot of people cheat with mail-in voting.” Trump has also suggested that widespread mail-in voting would pose a threat to Republicans' electoral success.

When people go to vote, “you go to a booth and you proudly display yourself,” the president said. The Trump campaign is also launching a multimillion-dollar legal campaign to block Democrats from changing voting rules.

Although Trump has claimed that mail-in voting is rife with corruption, there is no evidence to suggest that voter fraud exists on a wide scale anywhere in the election system. The president himself cast a mail-in ballot in Florida as recently as last month for that state's primary election.

Despite public health concerns surrounding in-person voting, Walden said it isn’t the federal government’s place to step in and tell a state how they should vote. And with Congress also working remotely amid the pandemic, he doesn’t believe something like this is fundamentally possible.

“It really is a state responsibility to run the elections, and I think it would be a real mess to suddenly federalize it,” Walden said. “And again, with just a few months to go. I mean fundamentally, Congress probably isn’t going to be back and voting on anything until May. And somehow we’re going to come together on a national vote-by-mail process by then? And voted and put it in place and fund it and get it up and running perfectly?”

— Melanie Zanona contribute to this report.