Think of Jackson like Erwin Rommell. He was a brilliant commander, but ultimately had to do what his superior told him. In this case, that was Lee. And Lee, while himself more than capable, made some questionable decisions as the war went on. Nevertheless, the issue is simple manpower. Rommell didn't have it; Jackson didn't have it. They might win in specific battles, but how many of their own forces fell vs the enemy?
Say Jackson loses 100 for every 200 he kills; that still means he'll run out of men MUCH faster than the Yankees will. That's the question you've to ask yourself. I began writing a TL where Jackson lives, goes on to help win the analogous-Gettysburg, but... the CSA still loses the war. After the amount of research I did, I'm of firm belief that the Brits and French will simply not intervene until such time as the Confederates are pounding down Washington - which they simply cannot do.
Sorry, Chap. End of story.
Now... I looked into it before I finally gave up on the TL, BUT here's a better question - what if Jackson lives... AND is sent to the Western theater? Against Grant and Sherman? I don't care who you are, Grant was not an imaginitive commander; he would have fit in well with a 20th century Russian or Chinese army of 'mass attack' tactics. He employed simple strategies and relied upon numbers. Meanwhile, he let Sherman off the leash. Sherman had the same mentality that Jackson did (war to the hilt, or "total war" - making the enemy howl and all that), but still I'd wager Jackson is a better battlefield commander.
His command in the west MIGHT - and only might - give the Union enough trouble and pause there to lengthen the war, but again... to what end? Numbers were still the factor. The only thing I see is if Jackson and Lee, in both theaters at about the same time, each crush a numerically superior force to such a degree that 1) Lincoln has a fit leading to... 2) the Union commanders getting sacked, thus 3) the Brits and French see an opportunity to take the USA down a peg.