I agree with dividing American and British literature. I might go:
Brit: Chaucer, Shakespeare, Dickens, Austen*
*or Kipling, maybe.
American: Twain, Poe, Steinbeck, Hemingway
Hmm, I feel like my familiarity with British Lit is somewhat lacking.
Can it just be one huge Hemingway sculpture? Or Hem with a rifle in hand, or a marlin hanging next to him!
I might be a little biased!
Shakespeare, Dickens, Twain, Whitman.
I’d bench Hemingway and Joyce to bring in Twain and Tolkein. Popularity isn’t everything, but it’s got to count for something. Oh, and Robert J Sawyer for the modern.
I’m currently wondering who my Four would be if I were judging, not on the basis of who were the greatest writers (or most influential or most popular or whatever), but who were the most iconic in appearance, so that their heads would look the best carved in stone into a big-ass mountain.
I think Shakespeare, Dickens, and Twain, at least, still have a pretty strong claim.
Make it Twain, Dickens, Hawthorne, and Vonnegut. Dueling moustaches!
I’d think Faulkner and Tennessee Williams would be shoo-ins. For the third, I’d probably pick either Capote or Poe and probably Poe, to give poetry a fair share of the glory.
But at the risk of falling over the cliff, how about the Crazy Horse statue of literature? Chief Joseph had a way with words but maybe not enough of a literary career. Will Rogers? Luke Warm Water?
Tolkein was not a great writer.
I would argue nor was Chaucer: his works just happened to survive.
Also, Whitman was cute but worthy of being carved into a mountain? C’mon.
Finally, if we separate Brits from Yanks, we also need a third mountain for the Paddies. Wilde, Swift, Yeats, Joyce, Beckett, etc.
Quite possibly, but he was a great storyteller.
So are Dan Brown, Tom Clancy and Jeffrey Archer. 
I think Brown and Clancy renounced any tenuous claim they might have had to greatness with a peanut allergy murder and having modern-day Japan declare war on the US respectively. 
I’ve never actually read any Archer, I’m just prejudiced against him because he’s such a lying little turd.
That would be “Sir lying little turd”, actually.
I like this idea. Almost enought to start a thread.
My votes go for Dickens, Faulkner, Twain and Jane Austen, because those are the Great Authors I’ve read and enjoyed. I can’t get into Joyce or Shakespeare or DH Lawrence.
I’d consider Edith Wharton and Joseph Conrad.
My Summer Beach Reading Rushmore has Carl Hiaasen, Ursula LeGuin, RA freaking Salvatore (leave me alone) and Elmore Leonard.
My Comics Rushmore has Neil Gaiman, Garth Ennis, Frank Miller and Alan Moore.
My Movie Critic Rushmore… oh, never mind.
A vote for female poets- Edna St. Vincent Millay & Emma Lazarus.
(At least an honorable mention plaque or something.)
Well, as a Paddy, I’m going to suggest for the ultimate Mount Rushmore, WB Yeats,GB Shaw, Samuel Beckett and Seamus Heaney.
Nobel Literature laureates all, and all Irish.
Irish chauvinism aside, I’d suggest Jane Austen, Joyce,Shakespeare and Conrad.
If we’re including poetry, I’m really surprised about so few mentions for Emily Dickinson.
I think Emily Dickinson should be on there somewhere.
And although she’s not a great writer of literature, because of what she helped accomplish with Uncle Tom’s Cabin (Lincoln said, “So you’re the little woman who made the great big war”), let’s consider Harriet Beecher Stowe.
Considering that Conrad didn’t learn English until he was an adult, he should get bonus points.
Wasn’t Shakespeare himself a member of that team?
Washington and Lincoln are turn of the 20th century?
And Mark Twain is the quintessential American author-- If any American at all makes it onto the list, it has to be him. Chaucer, meanwhile, is arguable: He’s undeniably important, but it depends on what we mean by “English language”. The language of Chaucer is not the same language as that of Shakespeare, Twain, or us.
I wouldn’t quite put him in my top 4, But I’d put Asimov way above a lot of these other suggestion if I had the chisel.
I’d love to believe the story that Shakespeare hid his own name in Psalm 46, but it’s very unlikely that he was involved with the project at all.