For caricature vibe, I would go with Broforce, which is my July 4th holiday game of choice. Such a fun and funny ridiculous game. Of course, not a USA setting but a very USA! USA! vibe.
For setting, I would go with Interstate '76 on the PC. Fictional, alternate "American Southwest." Driving around the desert in muscle cars with mounted guns.
As others said, the better TMNT games in general do well with the setting, and good call on Freedom Fighters.
Need to look through my game collection for other levels to highlight.
Edit: Just thought of a couple more; The Bureau, very cool Cold War/60s Gman-American setting. And Zombies Ate My Neighbors; very Anywhere, USA town thing going.