My understanding is that as of now dual isn't possible. I think there's a decent chance that at some point it will be. But part of me wonders if it doesn't change and I do that would I forfeit all my social security yadda yadda? Stuff like that. Granted social security won't be there for me, or it'll be worth a buck fiddy but that's not my point. I don't care that much about not voting here. I wonder if that would theoretically mean I have to leave the country. Etc
getting a dual citizenship is possible if you're born with it--I should know, I've got one. Beyond that it gets much, much harder, because gaining citizenship in an EU country (which is what I assume you meant by a Euro country) is not easy, much like gaining citizenship over here.
Now, I know when my Mom got her US citizenship, she had to renounce her previous one, but that was a decade+ ago and she was already here with my Dad--who was born here.
Just keep your head up and know it's going to probably be a long and arduous process.
And be careful, you might just end up a socialist!