I agree with those who say that LBJ's absence (and Jackson's Presence) on the Dem ticket probably swings the election Nixon's way and even if this doesn't happen, JFK's schedule is likely to be butterflied due in part to Jackson being VP and partly due to LBJ still presumerably being Senate Majority leader.
In the unlikely event that Jackson does become president on Nov 22nd 1963 however, he'd probably do much the same as LBJ re 'Nam' and the Great Society. I'd imagine some alternate version of the Civel Rights bill passes. Jackson would win in 64 for the same reasons LBJ did historically-CR being implimented, the economy doing okay and the JFK assassination giving him a sympathy boost. Not sure who he'd choose as his running mate though.
I do think Jackson's Vietnam polecy will be as unpopular as Jonson's, though whether he'd decide not to run in 68 is anyone's guess.
That said, there are a few scenarios where Jackson could become president:
(1) 1976, if he manages to overcome Carter and co in the primaries,
(2) 1976 in a TL where Watergate is successfully covered up,
(3) 1980, after a Ford/Reagan presidency,
(4) 1964/68, in a Nixon wins in 1960 scenario. I think 2 and 4 are the most likely out of those myself.