Actually a governor has some say on abortion. Sure, they can't sign a bill banning abortion, but there are reasonable restrictions that can be placed on abortion. For example, cutting any state funds to Planned Parenthood, changing Texas's parental notification abortion law into a parental consent law, and blocking any state plan promoting stem cell research.
I take it you are not familiar with the Texas system? We may have the weakest governor in the US. Our Lt. Governor is the power in the state and the Governor has only two real powers. The veto, which Perry uses a great deal, though he cannot tell you why, and the bully pulpit, at which he is 100% ineffective.
changing Texas's parental notification abortion law into a parental consent law