Albuquerque to Rio? Damn! Can't decide if I should warn you not to attempt it or beg to go with you!
I will point out that you won't be able to drive the whole way, because a section of the highway (across the Colombia - Panama border) has never been built. There is allegedly a car ferry, but I have no idea how reliable that is.
You'll need to do a LOT of research on Mexico because some sections are VERY dangerous these days. Learn a few emergency evasive driving skills, and consider carrying a weapon (and know how to use it).
No idea what route you're planning to take in South America, but once again you'll need to do a lot of research on road conditions, safety, etc when crossing from the west coast to the east.
The problem will not be anti-American sentiment per se, but general mistrust of outsiders when traveling through out-of-the-way places (in drug producing regions they'll assume you're DEA or CIA), as well as the fact that you'll be viewed as a piggy bank on wheels - your shoes are probably worth more than the locals make in a month.