There isn’t a national law.
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In 1993, Congress passed the National Voter Registration Act (NVRA).
NATIONAL per your own post.
“In 1993, Congress passed the National Voter Registration Act (NVRA). The NVRA pioneered a new way of registering to vote in America. It required most states to provide citizens with an opportunity to register to vote when applying for or renewing a driver’s license at a department of motor vehicles (DMV) or other designated state agencies. Because of the requirement for DMVs to participate in voter registration, the NVRA is often referred to as “motor-voter.”
This is not related to a national voter ID, it was a terrible law assisting with election fraud, and I’m sure that’s what it was designed to do.