One aspect I'm not seeing mentioned in other comments: ID is currently handled at the state level. A lot of Americans object to having a federal ID and if you required ID for non local elections (federal elections -- ie countrywide or national elections, like voting for the President), then you will run into problems because there is no standard national ID. If you required ID at the federal level, then you have to decide what constitutes acceptable ID and this potentially serves as regulation on valid state ID that I don't believe currently exists.

If you try to move to a federal ID, you de facto need to replace a bunch of state run offices with federal offices. This would not be an easy transition at all. It would be easier to create federal regulations and require states to alter their state ID to comply by X date, but states tend to resist that kind of interference from the federal government.

The US is a little bit like a country of countries. It would be a little bit like requiring an EU ID and European countries objecting.