After Mary Bailey served as elected governor, he won a later election and became governor. On May 19, 2002, he called the show Frame Up and talked to The Yes Guy and said he hopes Homer will "fry." He presumably loses the election in 2002 or does not run, as Mary Bailey is elected governor again. However before this the Springfield Republican Party in the episode "Brawl in the Family" scrapes every anti-pollution law "in the book", and because it was in his state during his term in office it is assumed he approved of this.
Possible Political Party
Mary Bailey won the 1986, 1990 and 2002 elections, so it's likely she ran in 1998 but lost and ran again in 2002 and won. Because Mary Bailey is a Democrat, supposing she ran against him, he would presumably be a Republican. Additionally the Springfield Republican Party tried to scrap every anti-pollution law in the book during his term, so it is assumed he is Republican because he supports this in his State.
Behind the Laughter
The only reason he couldn't be Mary Bailey is because when he called The Yes Guy, The Yes Guy implicates that the Governor is male by saying "The Governor says he hopes you're a twitcher" when referring to Homer.