The problem isn't the name. America has an absolutely huge number of Christian Fundamentalists and Evangelicals who honestly believe that a national ID card is the Mark of the Beast that's talked about in Revelation 13:16-17. Even mentioning it as a politician will cause large sections of the country to start referring to you as the Anti-Christ (it's not even political: it happened with Bill Clinton and it happened with Bush just the same).
The people who believe this vote at a much higher rate than the people who don't. And even the people who don't directly believe it, many of them are influenced by the people who do. "I don't actually believe Politician X is the actual Anti-Christ, but Preacher Y does make a good point about their tax policy..."
Anything new that could be called a "national ID" is going to be met with a lot of money saying it's the Mark of the Beast.