Your federal ID would do exactly nothing additional above and beyond the current NICS check used by FFLs currently. The current system has the advantage of being able to pick up any disqualifying event that has happened up to date. Your ID, I assume wouldn't need to be renewed monthly, right? So you have a clean background check done, ID card issued, then get convicted of a felony. 1 year later you walk into a gun shop and buy a gun with your ID card.
Also, requiring an ID that costs money as a prerequisite to vote infringes on the right to vote. The homeless guy living in a shelter has the same right to vote as you or I do. There should be federal legislation specifically prohibiting states from requiring this. In person voter fraud is virtually non-existent.