What are the sources of a possible victory for the CSA?
1). Maryland, Missouri and Kentucky secede. Missouri was contested for most of the war, but the Union maintained dominance. Kentucky and Maryland were effectively in the Union column by early 1862. Given Lincoln's caution in not giving them a major reason to secede and their economic ties to the Union, the chance looks like slim to none.
2). Foreign intervention. Essentially, this means Great Britain. Lincoln was careful with them. Great Britain did not have a major reason to intervene. Finally, the emancipation proclaimation made intervention by Britain nearly impossible. This avenue of victory looks very low also,
3). Military victory. This meant destroying a major Union army or two. The CSA came closest at Chickamauga but failed even there. CW armies took quite a bit to destroy. It really never happened on the battlefield. It came close at Pea Ridge and Nashville but even there the remnants escaped.
The other chance was a successful invasion of the North. Given the difficulty the Union had invading the CSA with much greater resources and organization, this looks pretty low. I would say a military victory is pretty low also.
4). By the end of 1863, the CSA could no longer credibly won a military victory. However, for Lincoln to be elected in 1864, the Union had to show decisive progress towards winning a military victory. Election of a democrat probably meant a negotiated peace. This was by far the biggest chance. It hinges on two possibilities. First off would enough Union veterans reenlist to keep the core of the Union armies? Grant and Sherman both put a major effort in encouraging reenlistment and it worked.
The second was would Grant and Sherman both push hard for victory? Many Union generals were slow to start and quick to give up. If either got the slows, the other would face almost insurmountable odds. The thing was they pushed onto victory. Sure it looked bad in August 1864 but after that Sheridan destroyed Early's army in the valley. Farragut took Mobile Bay, Sherman took Atlanta and Grant pinned Lee at Petersburg.
It became obvious that the Union was at the verge of victory and Lincoln was elected again.
The chance of Grant and or Sherman faltering or Lincoln ceasing to support them can not be calculated. Given Union resolve and competency, they would do enough to win the election in 1864.
In my mind, the chances of victory for the CSA Look highest by hanging on without major Union victories in 1864.
The problem is it looks as if given political skill from Lincoln, Union resolve, and competent persistence by Grant and Sherman, Union victory now looks nearly inevitable. But relying on three men to perform is rather dicey. Of course, had Grant or Sherman faltered perhaps Meade or Thomas would have come through.
It is not popular for Union adherents to admit that victory was that dependent on performance from key people.. It is also not popular among CSA fans to admit that given Union leadership coming through, their cause would be a long shot. They kind of seem to like to think that only a few CSA generals like Lee and Jackson could perform.