You didn't say if english was your native language, and I'm Canadian, so cannot advise you regarding the US situation, but here's what I've observed from Canada.
I have seen several students attempt ATC when english was not their first language, and they have a far more difficult time with the training.
First of all you must obviously speak english clearly and well enough to be understandable for obvious reasons. Too many "says agains" compound quickly into a mess and make things frustrating for everyone involved. The other factor I've noticed, and I hope this makes sense, is that you have to think in english. Students who think in their native language and then have to translate for themselves are starting off in a disadvantaged position and don't do as well.
It is certainly something that can be accomplished. I don't live in Quebec, but clearly there are plently of controllers who speak two languages, and are required to do so in that province, I'm just suggesting it will be an additional hurdle you'll have to consider in the US unilingual ATC system.
Hope this help to some degree. As for citizen requirements, why don't you just email the FAA.