If the North and the President are prepared to intervene immediately, then it's unlikely any slave state would declare secession.
For one thing, it implies that the President is absolutely unsympathetic to slave-state demands, and also that the slave states didn't declare secession before he took office.
I'm not sure it really implies that last bit. Consider that the initial seceding states did so before Lincoln was actually sworn in, because they believed he was, well... absolutely unsympathetic to slave-state demands.
South Carolina, Mississippi, Florida, Alabama, Georgia, Louisiana and Texas seceded between his election and his inauguation. One may reason that this would have happened the same way if a more radical Northerner was somehow elected, or Lincoln was somehow more radical.
On February 7, 1861, those seceded states adopted a provisional constitution.
On March 4, 1861, Lincoln was sworn in.
On March 11, 1861, the seven seceded states adopted the Confederate Constitution.
It seems unlikely that anyone could, given that timeframe, have launched a military invasion to prevent the Confederacy from being oficially created on March 11th. But supposing a president (be it Lincoln or someone else) willing to attack at once, the newborn Confederacy could have been crushed very swiftly.
I'm not sure about this, but is Lincoln (on anyone replacing him) in a position to prepare an invasion force before his is inaugurated, as president-elect? If he is, he can start as soon as SC secedes, and have his army start marching the moment he takes office. The sevem seceded states, barely organized, would not stand a chance. And considering that, I don't think any additional states (Virginia, Arkansas, Tennessee, North Carolina) will opt to secede.
It would be a very short war. Would that count,
Kovalenko?