Government or private sector background checks on tens and hundreds of million of persons just because they want to get on a plane? Sounds like a nightmare that won't accomplish anything useful.
How extensive will the background checks be? How often will they be done? Who will pay for them? What happens to people who "fail"?
This sounds like an invitation to an even greater surveillance society. No thanks. I'm not thrilled about dealing with the state DMVs a good part of the time. I certainly don't want to deal with a monster-size federal-equivalent of the DMV. Isn't the IRS enough for the average citizen/traveller?