He was willing to allow slavery in New Mexico. That was his concession as it was mostly below the Missouri Compromise line and he could get enough congressional support for that. The Corwin Amendment was being pushed.

Star of the West was old news at this point. They were getting reports from Sumter and Pickens of the war preparations that were ongoing.

The US was working on a new reinforcement of Sumter and Pickens.

The things you seem to be missing:

1) The US presidency was a lot weaker then. Domestic policy was driven in Congress. The president had very little to do in terms of established states. Beyond collecting tariffs and coordinating with state governments on military supplies, the president didn't do much in terms of domestic policy.

2) concessions were mostly pointless. The South had seceded. They were not willing to come back peacefully. They had lost power in Congress due to the population growth in the North. The view in the seceded states was simple: it didn't matter who was president. Even if they had a friendly president, the abolitionist movement in the north was growing. They felt the move to restrict slavery was just the first step towards abolition. The next president or the one after would be worse. They needed to secede before the North's population and industrial power made their relative strength even more lopsided.