Old Hickory had little trouble with the idea of Postmasters destroying “inflammatory” abolitionist publications as a denial of First Amendment rights. The issue of banning the abolitionist pamphlets illustrated a federalist tension not resolved for another century.
Jackson was worried that an executive order regarding the destruction of the pamphlets would be held unconstitutional if challenged, but the alternative was to have the States pass statutes authorizing the postmasters to destroy the pamphlets. Jackson didn’t like the idea of state authority over Federal officers; bad precedent. Calhoun knew the First Amendment didn’t apply to state action, but didn’t like the idea of an executive order to the Postmasters as an infringement on his concept of State’s Rights. So in the end, for perhaps the wrong reasons, the right thing was done; Nothing.
But then, I'm probably violating Henkster's Law.