One thing to understand is that under the US Constitution, each state controls its own electors to some extent, although certain requirements can be made federally. The rules can vary by state to some degree.
In Florida, I did once get a voter's ID card when I registered or confirmed registration to vote, but they also tend to accept driver's licenses. For all I know (I haven't tried), my security officer's license might even work for it (although I doubt it somewhat since it doesn't list my address).
As for the opposition to the Voter ID law proposals, from what I recall at the moment of the arguments, it boils down to a belief that it would be a shadow poll tax, either directly (if it requires DL or state issued photo ID that costs money, thus impacting the impoverished) or indirectly (forcing people with limited transportation means to spend fare money to go to offices to get/renew such IDs, or making it impossible if they work regular jobs that keep them from getting to the office while it's open).
The accusations extend beyond voter ID as well. IIRC it was North Carolina that some time ago ended early voting on Sundays, and it was noted that it was the practice of African-American church communities to organize voting drives following their Sunday services.
Personally, I'm fine with voter IDs, but I don't want any chicanery with them. Make them free, and make it easy for any citizen to get one. For instance, in Seminole County FL, I registered online (back in 2014 when I moved back into the county from Orange County). So long as you require something like a valid social security number it should work well enough. Not 100% fraud proof, but
what is 100% fraud proof?