The Vector Gambit is 1 c4 d5 2 cxd5 c6.  I am confused about what to do as white vs the Vector Gambit.  The primary alternative to 2 cxd5 would be to transpose to the Queen's Gambit.  My feeling is white should be able to take and get an advantage.  However, 3 dxc6 Nxc6 gives black dangerous play and 3 d4 or 3 Nc3 cxd5 4 d4 simply transpose to the Slav Exchange V which is as dry as dry can be.  Tracing the line back, I'm doubting the move 1 c4.  

Black gets some play for the pawn, sure, but you will never refute a gambit by declining it. 

Well if you don't take the pawn then Black is going to get a pawn on d5 for free. You really can't allow that in the English unless you're getting something for it. You really have to take that pawn. It's basically a Smith-Morra Gambit for Black a tempo down so just develop in a compact way.

I would try to get a e3-d4 pawn structure which would cut down on a lot of those open file tricks that Black would like to play. I'm not sure about when and where to develop the c1 bishop.

actually, according to Reti, King's Gambit is pretty much refuted by Falkbeer's Counter-Gambit.