I disagree with your premise that it has to have the backing of those using it--it just has to not be opposed by the majority of those using it. This may seem like a subtle distinction, but I think it is an important one. From what I've seen, many (and I mean a lot of) Americans are oblivious or just plain don't care--and we can count them out of the equation from the get-go.
From the limited exposure I've had to nuke plants, the general consensus of those who live around the one nearest to me seems like they support the plant and are not unhappy having it nearby--it is clean, provides ~1000 jobs (and the employees live in the local community) and provide huge amounts of property taxes to the local jurisdictions.
Granted, building a new nuclear plant would probably generate a huge NIMBY stink, but expanding at existing locations would be much more palatable to the communites involved.
I read an article a while back that said the general opinion of nuclear was on the rise--I don't have it handy so I can't quote the numbers. But, Patrick Moore, one of the founders of Greenpeace, has actually flip-flopped and now supports nuclear (
article here). And if this can happen, then yes, I think nuclear can win enough support stage a resurgence.