"I cannot think of the deep sea without
shuddering at the nameless things that may at this very moment be crawling and floundering on its slimy bed, worshipping their ancient stone idols and carving their own detestable likenesses on submarine obelisks of
water-soaked granite. I dream of a day when they may rise above the billows to drag down in their reeking talons the remnants of puny, war-exhausted mankind -- of a day when the land shall sink, and the dark ocean floor shall ascend amidst universal pandemonium."
- HP Lovecraft, Dagon
A pure fantasy map - Lovecraftian, that is.
No fear, though; humanity, as implied by the title, survives. 
1. If Cthulhu awakes, we're boned.  But he's still sleeping.
2. The Deep Ones are made of meat, as are their monster servants. The bigger they are, the better military targets they make. And their weapons are mostly of the pointy metal thing variety. There are billions of them, which does give them a bit of an advantage initially in thinly-armed areas.
3. Sure, they have black magic. But Arkham University and various third-world witch-doctors are on that. (Remember in the 'Shadow over Innsmouth" the Deep Ones in the Pacific were baffled by a bunch of Polynesians with star-stones).
4. Shoggoths are, admittedly, a problem - which calls for high explosives followed by flamethrower mop-up. The shoggoths that serve the Deep Ones are neither as smart nor as huge as those under Antarctica. (If they were, it would soon be by bye Deep Ones).
5. The eventual outcome is MAD. We can't find all their cities, and irradiating the oceans would kill us too. Also, they can summon the Outer Gods - which will kill everyone save Cthulhu and any other Great Old Ones lying about. (hey, if a half-non human hillbilly with access to a good library could do it..)
(My assumption is that a modus vivendi will be arrived at before the world is stripped clean and yanked into a violet-lit infinite abyss).
 FOR NOW
 My personal no-prize theory? If the Big C just needs somebody to knock on his door for him to wake up, why all the elaborate cultist stuff? No, he slept through the rising and sinking of R'Yleh: he just grew close enough to wakefulness to kill the guys who messed up his ressurrection with a materalized dream of himself: just good ol' ectoplasm, not cosmic monster-flesh. The actual Cthulhu sneers at speeding steamboats.