That's actually not true.
You may register to vote any time after you have reached the age of 17 years and 10 months so that your registration can be processed in time for an election falling on or after you turn 18 years old.
Other voter eligibility requirements include:
You must be a citizen of the United States.
You must reside in the county where you are registering.
You must NOT be a convicted felon who is currently incarcerated, on parole, or probation.*
You must NOT have been declared mentally incompetent in a court of law.
Once you have completed your period of incarceration, parole, and/or probation your voting rights are restored. You may need to re-register to vote.
My point is just having a national ID does not automatically mean that you are eligible to vote. And I could be wrong, but I think David Dennison wants everyone in the US to have a national ID, whether they are here legally or not.