The South had that complaint in the 1830s because it was true: tariffs fell mainly on the exporting section: the South. Between 2/3 and 90% of tariff revenue was connected at southern ports, chiefly Charleston and New Orleans.
John Taylor of Caroline (R-VA) said he was approached by very prominent northern senators (one a Boston-born New Yorker, one from Connecticut) about breaking up the Union. The idea remained alive in the mind of at least one of them, Massachusetts’ Timothy Pickering, well into the 19th century. Eventually Gouverneur Morris, the man who actually wrote the Constitution, supported a partition of the country too. Jeffersonians’ electoral success, helped by the poor timing of the Hartford Convention, seems to have doomed the cause to failure.