Originally Posted by The Question
Worse than suspicious. Not only would you have people blaming him as equally responsible for the destruction his battle with Zod caused (wether or not you as a viewer think he shares any responsibility doesn't change the fact that that's how a lot of people would react), but there's the fact that Zod flat out told the entire world that the only reason the Kryptonians came to Earth was because Superman was there. A huge swath of the population are going to place all the blame squarely on him. Over time, it might subside if he never does anything controversial and just saves people from disasters (and does that a lot), but within six months of the invasion there's going to be a huge amount of public outcry demanding his head.
Yeah, it'd make for magnificent grist in the sequel. Just a pity in my book this wasn't teased out in the movie's closing moments.