I certainly agree that Grant's leadership made the military difference in the Civil War.
The South could never have won the War. The North, however, became war weary over time. There was a time in 1864 when McClellan was believed likely to unseat Lincoln, and the South was holding out for this in the realistic hope that such an event would end in a negotiated peace of some kind. Grant's leadership was a key ingredient in giving the North hope for victory and belief that it was worth it.
I don't know as much about the fighting of the Civil War itself as this or the original poster, but I've suspected that had the South maintained a purely defensive strategy (Gettysburg is up in Pennsylvania after all) they could have waited out the Northern Population.
Of course, putting a trench all across the Mason-Dixon line would have been impossible, so what do I know?