Gore probably governs simelarly to Clinton. No idea who his Veep might be-Dick Gephart maybe?
Clinton dying 2 months before the mid-terms means that the 'Contract With America' is probably delayed somewhat.
This also means that in 1996, it'll be the ultimate corrisma clash-Gore verses Dole! and you thought the 96 election season was boring in OTL? Never the less, the economy is too good for there to be any change in the Whitehouse and Gore still wins.
No Clinton means no Monica scandle-and therefore no intreague in to the activities of the speaker of the house-so Newt remains Republican House leader for a while longer.
He might try the contract in 1998-and without the attempted impeachment of Clinton causing people to ralley around the president, the GOP might be successful, only 4 years later.
Not sure who'd run in 2000. The sympathy boost might just be enough to make Ann Richards hang on to the Governer's mantion in Texas, in which case we can rule out Bush as the 2000 nominee.
Assuming Gephart is the VP, he probably gets the 2000 nomination, though I guess it's possible for Hillary to pull an RFK 68 in 2000 if she gets herself elected to something after Bill's death.
If Gephart is the nominee (which is more than likely in this scenario), I think he'd probably lose to Bush, Mckaine or whoever the GOP nominee is.