The administration actually thought the presence of union troops would inspire southern unionists to rally around the flag. Instead, it steeled the resolve of the rebels to drag them into the confederacy.
There were enough cooler heads in Missouri, Kentucky and Maryland to prevent them from following the same sorry path, but a deescalation of the Fort Sumter situation might have prevented a catastrophic war and given the unionist sentiment in the south a little more time to organize.
“...and given the unionist sentiment in the south a little more time to organize.”
Not to mention the constitutionalist sentiment in the north.