Some Americans, particularly evangelical Christians and libertarians, are vehemently against the idea of a national identification system. To them it’s either the beginning of a New World Order government or the Mark of the Beast or both. So having a national ID card will never fly. Social Security Numbers aren’t even supposed to be used for identification, despite the fact that they’re used that way everywhere.
There’s also the case that not everyone has an ID. Racist southern states, for example, enact voter ID laws and then remove all places where you can get an ID from majority black areas. Having to show an ID to vote is, therefore, going to disenfranchise some people. You could get around this by broadening valid identification to include simply bringing a piece of mail with your name and address on it.
Actually SSN’s ARE supposed to be used that way now. It wasn’t intended when the system started because it was difficult to get everyone one. But once the system was established they started pushing federal agencies to use them. Then in the ‘60’s when the digital revolution began it just made sense to use them. But the law has been changed since 1943. The new cards don’t even have that line on them anymore.
