Honestly?
Probably laugh as he got ripped to shreds by the police and/or national guard.
I'd find it hilarious that old HP saw this coming, but at the same time didn't see the whole picture.
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Understand that part of the horror of the stories is the irrelevence of humanity and the idea that we peaked as far as we could go and it was insignifigant in the scheme of things. We have come further than HP Lovecraft could ever have imagined and a lot of what we can do is far in excess of what a lot of his aliens and eldrich horrors could accomplish in a lot of respects (though not all).
Cthulhu is not a god, but rather a high priest of a number of alien dieties. He came to earth in our pre-history with humans as his slaves. He wound up waging a war against The Great Race Of Yith which defeated him and his species and imprisoned them in eternal slumber after many epic battles. The Great Race Of Yith, who were a group of mind-projecting time travellers were themselves semi-overcome by the Flying Polyps, they pretty much returned their bodies to their own time/world and left the cone headed beings they possessed to fend for themselves, and being more or less mindless they were overrun and the civilization the Yithians built fell into disrepair.
The result being that the humans, who were numerous, wound up being the most advanced creatures on the planet, and slowly came to dominance, though by these concepts we also lost a lot of what we were. In a story HP Lovecraft edited called "The Mound" a human civilization that was fairly untouched was revealed to have been living underground and the people there had things we forgot (but could learn) like line of sight telepathy, and the abillity to turn ourselves and other objects intangible. Not to mention the abillity (apparently though science) to reanimate the dead.
At any rate, the weapons that humanity possesses right now are far more powerful than those of the 1920s and even more powerful than those used by races like the Yithians and Mi-Go in many respects. Sure, we can't psionically time travel, but in terms of raw destructive output our current technology is greater than them all. The old comment from the CoC RPG about "what would happen if you nuked Cthulhu? He'd reform 15 minutes later, radioactive and mad" is a bad joke and doesn't really match the lore.
Right now we've got guns that could blow holes the size of a basketball in Cthulhu from close to a mile away, to say nothing of tanks, artillery, and even assault weapons and armored vehicles used by the police. A gang banger with an Uzi would absolutly shred a lot of the mythos monsters (albiet not all of them).
Pretty much Cthulhu would rise up, and last roughly long enough for someone to realize that he was a potential threat and respond in force, at which point he'd be hit by so much firepower that he'd actually miss the Yithians that kicked his butt the last time.
As far as insanity goes, while some sources have turned it into something of a joke, where Cthulhu is treated as driving people insane just by looking at him, in reality the idea of the insanity surrounding the Mythos in the novels was the realization that such things could exist compare to the psyche of the time. While a lot of people would be somewhat shocked to see such things, today people are jaded enough, and familiar enough with concepts like space aliens and monsters wher we would adapt fairly quickly as opposed to having our mind shredded that something as intelligent as us (or more so) and obviously inhuman could possibly exist. Even those who don't believe in aliens, at least acknowlege the hypothetical possibility nowadays and wouldn't be shattered to the point of dysfunction if proven wrong.
Ah well, enough rambling. This is probably too serious an answer for the discussion.