Yes, in the sense that the President has a duty to see that all Federal law is properly enforced. If South Carolina, Georgia, Florida, Alabama, Mississippi, Louisiana and Texas were ever to return to the fold, the Morrill Tariff would have to be observed and respected in each of those states. Except in time of war or national emergency, the President has no authority to negotiate or set aside enforcement of Federal law.
The question isn't whether Abraham Lincoln favored a high protective tariff or not. He always did, and never apologized to anyone for it. Lincoln's advocacy of a high protective tariff probably helped Republican ticket carry states like Pennsylvania. HIs position remained unpopular in agricultural sections of the North.
The Morrill Tariff passed the Senate easily because seats normally occupied by 14 senators representing these states were vacant.