When the Confederates failed to bottle up the Union at Chattanooga for the whole winter of 1863-64 they lost their big chance to present a Georgia stalemate to the electorate for the 1864 election. McClellan might have had a shot against Lincoln had Sherman still been bogged down in the rugged terrain of north Georgia.
The Confederates, under Braxton Bragg, HAD the Union bottled up in Chattanooga (with Union general William Rosecrans in charge). It took the War Department moving Grant to Chattanooga, his replacing Rosecrans with General George Thomas, their opening up a supply line to the city, and two well-fought (though not so well managed) battles to relieve the siege.
Sherman's ability to move beyond North Georgia was helped in part by an indecisive Joseph E. Johnston (who had replaced Bragg). Johnston was never a favorite of President jefferson Davis, who eventually replaced him with John Bell Hood (just prior to the Battle of Peachtree Creek). Hood soon retreated from Atlanta moving North-West, and opened the door for Sherman's subsequent March to the Sea.