I can't help but cringe whenever politically motivated people throw around talking points they heard on their favorite disinformation cable network.
The reason why we don't have a proper national id card is primarily a result of state's rights vs fed rights and to prevent centralization of power. But centralization of power has happened regardless so I'm sure we'll be getting national id cards eventually.
Historically, it was the Democrats ( the party of the South ) who were anti-national id card. The republicans were the party of the northeast elites. So if you want to blame anyone, blame the democratic party because they are why we don't have a national id card system.