Why did Lincoln say, "Vicksburg is the key. The war can never be brought to a close until the key is in our pocket"?
I think that Lincoln understood the political and military significance of Vicksburg. While Gettysburg is often seen as the turning point of the war, it was never envisioned to be a battle of importance. It resulted as one, but it was never designed to serve in that capacity. However, both sides understood the importance of Vicksburg. It was through the capture of Vicksburg that Lincoln understood the war could decisively turn in favor of the Confederates. Initially, Lincoln understood that Vicksburg was so important to place in his column or "pocket" because the South relied so heavily on it. Lincoln understood the strategic and political importance of capturing something that meant so much to his adversary. Consider Jefferson Davis' assessment of Vicksburg:
Vicksburg is the nail head that holds the South's two halves together.
Lincoln understood that if the North was able to capture Vicksburg it would significantly weaken the South by taking away something of so much importance. It would take away a staging ground for the South and give the North a location from which advancement into the South could be practical by giving them control of the Mississippi River, thereby limiting the South's military activities. In this, Lincoln understood that the war could only be feasibly seen as in favor of the Union if Vicksburg had been captured.