Unless the USPS is deliberately disabled, mail in ballots won’t be a problem for the Post Office. There are about 160 million registered voters. If every one of them voted by mail on the same day, that’s less than a morning’s work for the US Post Office. On an average day, they deliver almost 500 million pieces of mail (and much, much more during the holidays)!

US Post Office: ONE DAY IN THE LIFE OF THE U.S. POSTAL SERVICE

USPS Office of the Inspector General: Assessment of the U.S. Postal Service’s Service Performance and Costs