I think it's possible to ban guns and remove them from the populace. But this would have to be done gradually over time, starting with tighter restrictions, more stringent checks and psychological profiles, and maybe by making certain types of guns more difficult to be purchased.
Start by slowly but steadily limiting the flow of new guns into the existing ecosystem.
Introduce buy-back programs that let people trade in guns for cash.
And most difficulty, shape the culture of future generations of American children to associate guns with bad things. It's going to take institutional change in educating future populace as well as introducing, gradually new rules.
This could take a century or two. It might not happen in our generation but it could be more likely to happen in future generations. We just have to engineer and reshape our culture in a specific direction.
edit: I guess what I'm saying is that an out-right ban is unrealistic, but you could take measures to slowly reduce the stream of new guns to a trickle and THEN try to deal with eliminating the existing pool.