It depends.
I think the scenario you're describing, in which one person instantly and single-handedly saves the world from an obvious disaster, is far enough beyond the pale that a hard-science answer based on real research isn't very possible. Our biggest Obvious Looming Disasters-- the Cold War, Nazi Germany-- were mitigated by lots of regular people working together. Obvious is key here, because if most people don't recognize the threat, then the person who claims to mitigate it isn't likely to receive much credit. And while there have been people with abilities that could* be considered superhuman, they're usually treated as forgettable curiosities (see "idiot savants").
However, the reaction of the general public to a superhuman has been tackled before in fiction, so here are some possible public attitudes toward a superhuman and an example of each. All of these assume that your superhuman is a decent person overall and generally tries to do the right thing; if not, public perception could vary dramatically.
* Religious devotion: Batman v Superman (2016). A major theme in BvS is that <PERSON> is treated like a god. The movie even shows that god-status isn't ubiquitous, and some would likely see your superhuman as a false idol.
* Hostility: Batman v Superman. A second major theme in BvS is <PERSON>'s own treatment of <PERSON>. 494
He ignores the problem of whether <PERSON> is a real or false idol, and takes a <PERSON>'s Wager approach to the problem; the consequences of <PERSON> turning hostile are so dire that it needs to be treated as an "absolute certainty." (The flaws in his logic are addressed in this think piece, but that doesn't make it an unrealistic reaction.)
* Talisman/cultural icon: The Dark Knight (2008). In one scene, a would-be criminal sees the Batsymbol in the sky and decides not to go through with a drug deal, purely out of the threat of retaliation. (<PERSON> is not, strictly speaking, a superhuman, but he's treated as such by the superstitious and cowardly lot).
* Moneymaker: Spider-Man franchise. Spider-Man's most public critic, <PERSON>, treats the web-slinger not as a real threat but as a means to sell newspapers. By printing attention-grabbing headlines about this otherwise well-liked "menace," his sales increase dramatically. (This can be seen in the real world as well, by the prevalence of tabloid magazines that publish scandalous made-up drivel about famous people.)
* Dependence: The Powerpuff Girls. In the episode Too Pooped to Puff, the townsfolk become utterly dependent on the girls to save them; so much so, in fact, that they lose all basic motivation and treat devastating monsters as funny spectacles. While this is obviously an extreme example played for laughs, the presence of your superhuman might make world crises seem less scary to a lot of people.
*Skilled, yes; superhuman, no. 282