Leading some irregular cavalry on a scouting mission, Jenkins thought the city was vulnerable, and Ewell was getting ready to do it. The sooner II Corps gets up there, the more vulnerable it is. They might provide stiffer resistance than expected, but Jackson had the nerve to follow through on a risky plan, so it's certainly possible to imagine him putting the smoldering ruins of a state capital on the cover of everyone's Harpers Weekly.
Bragg pulled off the largest movement of troops by rail of the entire war when he shifted his base from Tupelo MS to Chattanooga TN; if things are quiet in JE Johnston's sector, have him spend the early summer fortifying the heights around the town, and shift Buckner or Hardee's corps to Vicksburg with ASJ to counter Grant once he cuts himself off from his supply lines. With Halleck as General in Chief, if Grant's risky move fails, he can really find himself in the doghouse.
If that works, and the AotP is as bloodied as OTL, shift Buckner/Hardee and Longstreet over to JEJ with ASJ and head for Nashville after blunting Rosencrans's attack on Chattanooga. If his army's still in good condition and Vicksburg isn't in dire straits, might also have Beauregard head for Tupelo or Corinth, and eventually Memphis.
Best case scenario, end of 1863: Confederates hold Nashville and Memphis, National Union/Republican governors of Ohio and Pennsylvania lose reelection. Union high command going into 1864 is Halleck for General in Chief, and Meade [unless replaced if Harrisburg falls], Rosencrans [ditto re: Nashville], Burnside, and Sherman for main army commanders.