There would probably be a (con)federalist pro-tariff mercantile party, and a states rights anti-industrial planter party. Kind of like a continuation of Cotton Whigs vs Jacksonian Democrats mixed with Federalist/Republican (or more Federales/Unitarios like in 19th century Argentina) debates over centralisation of the government, which would be necessary for the CSA to survive in the long term. One party would be isolationist/pro-British and another more pro-French and slavery expansionist in Mexico and possibly Cuba.
It is perhaps ironic is that Alexander Stephens, who had been a Whig, was almost Jeffersonian in his opposition to the policies of conscription and centralization from the Democrat Jefferson Davis. Possible that might have played out long-term in a reconfiguration of coalitions away from the patterns of the 1st and 2nd party systems.
