Voting is a guaranteed right of the US constitution, but there are some real barriers for some people for getting state issued ID. It's has a monetary cost, it expires, it now requires a birth certificate. If you're poor, older, or happened to have your birth hospital's or county office's records destroyed by a fire (not uncommon at all), you may not be able to get a valid, state-issued ID.
For instance, my mother was born to Irish parents with US citizenship through naturalization (granted under a law according citizenship to people who fought for the allies in WWII). When she moved to a new state and needed to renew her driver's license, it took months to get someone to accept her documents and explanation even though she had been a US citizen all her life (but born outside the country).
Whatever national ID system would be implemented, it would have to be bulletproof. Otherwise it could incidentally disenfranchise people.