Final answer:
The Union general fired by Lincoln for indecisiveness was George B. McClellan, who also ran against Lincoln in the 1864 Presidential election. He commanded the Army of the Potomac but was replaced due to his overcautious tactics.
Step-by-step explanation:
The Union general who was eventually fired by Lincoln for having the "slows" is George B. McClellan. He was the general in chief of the army and in direct command of the Army of the Potomac. McClellan's overcautious nature and reluctance to engage the enemy made him popular with his men but ultimately led to his dismissal, as President Lincoln and Secretary of War Edwin Stanton lost confidence in his willingness to take decisive actions against the Confederate forces. Eventually, McClellan would run against Lincoln in the 1864 Presidential election, indicating his significant role and recognition at the time.
General Robert E. Lee was the Confederate commander during the Seven Days battle, while General Ulysses S. Grant was the Union commander at Shiloh. Neither of these generals were displaced by Lincoln for indecisiveness, as was the case with McClellan.