Law Professor John J. Martin of Quinnipiac University has this essay, pointing out that Congress has no authority to set voter qualifications, even in federal elections. Article One lets Congress write laws on the “time, place and manner” of congressional elections. But those categories don’t include anything about voter eligibility. Therefore, the SAVE America bill recently passed by the U.S. House, mandating that only citizens can vote in federal elections, has no constitutional basis.
The article also points out that nineteen states let non-citizens vote during the 19th and early 20th centuries. Also currently 20 local governments allow non-citizens to vote in elections for their own officers.