Part of the culture in the sense of ‘mass’ maybe. But King’s writing is never quoted nor has he created any indelible characters that live apart from the page the way that Tom Sawyer, Huck Finn or Elizabeth Bennett do.
And the King characters that people think of are actually distinct actors’ performances which depart from his arid texts considerably. Jack Nicholson in The Shining and so forth.
I wouldn’t say King’s writing is never quoted. On average how many replies does it take for an H1N1 thread to have somebody mention Captain Trips. I hear a lot of people refer to mean dogs as “cujo”. The Pet Cemetery resurrection trope has become pretty common place both in horror and satire. Since I hang out with authors Annie Wilkes and Richard Bachman are characters frequently referred to. I probably hear references to King books 10 or 20 times more often than Twain.