The publishing world today is so different from when Dickens and Twain were publishing. It’s even significantly different from when Bradbury published his early classics. Not as many people read for pleasure any more, and the major publishing houses determine who’s books are going to be picked up by the casual reader because those authors books greet you when you walk in the book store. I’m afraid classic status will be determined by whose backlist the publisher can successfully repackage and resell.
It may be cynical, but I would say the “New Classic” authors will be those authors that you always find at the bookstore (or more significantly the grocery store). I’m not saying they are bad authors or that their works shouldn’t become classics just that the designation of classic will be influenced by the publisher more than it was in the past.