I'd ask for confirmed space on another carrier but at this hour I think it might be too late to get there any sooner. Most flights for South America all leave the United States around the same time. Personally I would've asked immediately if it would have been possible to put me on a flight to MIA or JFK and then put me on AA, RG, or even (gulp) AR.

At this point, though, I'd make sure they gave me a hotel room for the night at UA's expense and would then make sure to write a letter to UA. The form they will give you often will not provide you with anything meaningful. I would definitely recommend writing a letter and specifically asking for certain compensation.

Best of luck, and let us know how it turns out!