How was Sherman’s victory over Joseph Johnston around Atlanta significant to the Union’s presidential election of 1864?

Sherman's victory over Johnston because in the long run it helped to break the South's economy, will to fight, and overall army strength.
Militarily before Sherman's march to sea, The South had been stubbornly losing the Civil War even while winning battles and inflicting heavy casualties on the North. Heavy casualties mounted in the minds of the Northern people. The Northern people felt that they should be able to quickly end the Civil War or allow an independent South. Due to the struggles of the Northern armies, Sherman and Grant implemented a style of warfare known as total war. Sherman's goal was to march from Tennessee to Atlanta and then back up through the South to meet Grant. While on this march Sherman was to burn everything in his path as well as free the slaves. The one true Southern army in Sherman's path to stop him was commanded by Johnston. The defeat of Johnston allowed Sherman to run wild through the South and torch the economy as well as break the spirits of the people. This was a huge victory in the eyes of the Northerners and a huge loss for the South.
Politically at a time where the North was tired of war, this was a campaign which showed true results. Draft riots had broken out in the North and Northern democrats were calling for peace. Lincoln needed a quicker end to the war and Sherman was providing it by the March to sea. An end in sight in the Civil War would prove crucial to the re-election of Lincoln. Many people could now see that under Lincoln's leadership the country could be brought back together. This victory gave him the crucial votes and public support that he needed.

It looked like the Civil War was going badly for the North in the spring of 1864. Grant was taking heavy casualties while advancing on Richmond slowly through a series of battles in what would be known as the Wilderness campaign. The death tolls were staggering, with families scanning the newspapers daily to see if their loved ones appeared on the casualty rolls. The war had been going on since spring of 1861, and the South, despite having lost key battles in 1863, did not look to be any closer to surrendering. Democrats under the leadership of former leader of the Army of the Potomac, George McClellan, ran under a promise of ending the war. The mood among many Northerners was that if the South desired its independence that badly, then it should be allowed to go in peace.
Sherman captured Atlanta during the election season of 1864. Not counting Richmond, Atlanta was the most prized city in the South. It's Tredegar Iron Works produced much of the South's cannons; it was also a major financial and rail center for the region. Lincoln was extremely happy. He declared a day of thanksgiving for the Union. The end of the war appeared in sight, and the Peace Democrats suddenly looked like defeatists. Lincoln thought that he would lose the election, but instead he won with a majority of the popular vote.