"The inhabitants of the United States have, then, at present, properly speaking, no literature". Pt. II, Book I, Chapter 13.
Tocqueville published this in 1840, when it was no longer true. Emerson, Poe, Longfellow and Hawthorne had all published major work by this time. Dana's Two Years Before the Mast came out the same year.
But Tocqueville's visit to the United States took place in 1831 and 1832. Poe and Hawthorne had published, but to no audience. The big names we still read were William Cullen Bryant, James Fennimore Cooper, Washington Irving. Bryant wrote at least one perfect poem ("To a Waterfowl") and Irving wrote at least one perfect story ("The Legend of Sleepy Hollow"), but none of these writers are quite central to US literature any more. There was certainly a lot of publishing, much of it religious and political, but also novels and poetry. Anyone who can make it through Joel Barlow's epic Columbiad, or the selected poems of Washington Allston or Philip Freneau is made of tougher stuff than I.* See the Library of America anthology, American Poetry: The Nineteenth Century, Volume 1, for mind-numbing samples.
Tocqueville compares America's democratic literature to France's aristocratic literature, the mass audience to the select. He has a real insight - what America (or democracies in general) lose in refinement will be made up in volume. In other words, even if a massive amount of trash is produced, there will also occasionally be writers as good as Racine or Voltaire, just as a matter of probability. This seems pretty canny to me.
I am not sure what Tocqueville means when he talks about aristocratic literature - my guess is the 17th century classics like Racine and Corneille, but he never says. While he is in America, while he is writing Democracy in America, there is a real boom period in French literature and theater - Balzac, Hugo, de Musset, de Vigny. These writers, certainly vulgar Balzac, must be part of the democratization of French literature, part of the same phenomenon Tocqueville sees in America.
* Barlow's "Advice to a Raven in Russia" is actually pretty great.