What bad things would the "National ID" do that aren't already in place?
If John Smith who was born in Oregon moves to Idaho and wants to register to vote, it will be necessary for the state officials in Idaho to verify his birth records. How is having Oregon maintain the records better than having the federal government maintain them? If Oregon receives a records request, there will be no standardized way for it to verify that it is fetching the records at John Smith's request. Further, if the federal government demands John Smith's birth records, I wouldn't expect Oregon to refuse.
As it is, the federal government has Social Security records for the vast majority of citizens born in this country. The only citizens who would not have such records would be those whose parents never declared them as dependents. So most likely the IRS would have a pretty good idea of when and where John Smith was likely born, and would probably be able to verify that information with the state at will. So how is that different from having the federal government hold the information (or at least a verified copy of it)?
Well, let’s just say that, since the passage of the 16th and 17th Amendments, the federal government has assumed jurisdiction over more and more things in our lives. Why let it go any further?