Not a lot changes really. Calhoun would be 78 in 1860; he's hardly going to take a leading role in anything. Unless he does something totally unexpected like urging South Carolina against immediate secession, his role will be that of an elderly prophet feeling himself vindicated at last. Perhaps as a mark of respect he is elected to the Provisional Confederate Congress like John Tyler, but he's not going to be fit enough to actually take his seat. When he dies, he's given a state funeral by the Confederate government and his historical reputation is even worse than in OTL.