jdurg is right on, as far as I can tell. The Na+ and the bicarbonate should dissociate completely in aqueous solution, so there would be quite a lot of bicarbonate ions floating around to deprotonate water molecules. The pKa of carbonic acid is about 6 while the pKa of water is about 16. So, the equilibrium isn't very favorable, but it does shift enough to make the solution slightly alkaline.
Here is a more qualitative explanation in terms of Le Chattlier's principle:
Given the equilibrium
HCO3- + H2O <--- H2CO3 + OH-
Stressing the system by adding additional bicarbonate will cause the equilibrium to shift to relieve the stress, therefore shifting to the right, which produces more hydroxide.
I hope this all helps.