I doubt this would happen. Americans don't want a place that is as chaotic and corrupt. If they can get their act together there is a chance they could join, but until that happens there is no way it would happen.
Argentina is mostly white, Christian and doesn't have any part in the internecine blood feuds that roil South Asia or the middle east. Lots of land, and well educated. No history of slavery (well at least not like its neighbor Brazil). So, yeah, it'd be a great addition to the USA. I'd take it.
To expand on my previous point Argentina seems like one of America's most poorly governed states at the local level - New Jersey. High level of local corruption, etc. And NJ is full of Italians and so is Argentina. It'd be like admitting a giant-size NJ. I'll take it!