Lincoln worried about resupplying fort Sumter because he thought it would provoke war (which it did), since the Southerners would view this as a federal intrusion.
For the answer to the question above, it is the root of the aspect of what they call "federalism" within the country’s government system, it means that although power is shared between the federal government and the states, the federal government reigns supreme.
7 anitfederalist
8 federalist