Andrew & all,
You're also making assumptions about Clinton that I don't think hold up.
At this point Bill Clinton's record is not all that stellar. His big push in his first term was health care reform as led by his wife. That turned into such an epic disaster that it cost the Democrats the House. AND it burned any hope of actual health care reform for an entire generation.
That's not much to crow about for Bubba.
With the GOP in control of the House they throttled Bill Clinton to the point that he finally retreated from his liberal economic policies and gave it up for the Republicans. That brought about a definite economic boom for the nation.
In OTL, Billy Jeff was exceptionally adroit at laying claim to that boom as his own. This, when it was actually due to the Republicans forcing their economic agenda upon him.
So, in this ATL, Bill Clinton has not had the chance to fully develop his persona. Now he gets chased out of office for cheating on his wife. Once that ball starts rolling there will be huge changes on the Democratic side.
Yes, there'll be a backlash but there'll also be some massive "distancing" of the Democrats from their failed leader. That will make for an ugly "piling on" of one revelation after another. All to make the case that Bill Clinton "lied" to the Democrats so his failure is not therefore the _fault_ of the Democrats. To achieve this it will be essential for the Democrats to make sure that the public knows that Bill Clinton is damaged goods.
Thus a lot of the effort expended in OTL to keep such information away from the public will, instead, be expended to keep such information _TO_ the public. There'll be no behind the scenes suppression or damnation of witnesses to Bill Clinton's decades long sexual escapades. There'll be no inhibitions for "the truth" to come out about all the various other scandals the Clintons were involved in back there in Arkansas. The various land deals and political payoffs that Billy Jeff benefited from as governor will, in this ATL, come out into the light of day like never before.
Yes, there'll be a backlash amongst the Democratic Party leadership against the GOP. But that will be a much slower burn and be aimed at Republican politicans and their political agenda in general - not amongst the general public.
There's a strong case to be made that the reason the GOP went after Clinton so hard was due to the Democrats having gone after Nixon so hard. That's a twenty year gap. So, if the same holds true, you could expect the Democrats to be seeking their cold revenge on the GOP as of the 2008 election cycle!
So, in this ATL, Clinton is out in 1998 and Gore gets to sit behind the Big Desk for reals. He is facing some truly dismal prospects as the GOP will be surging all around him. AND when the Dot.Com bubble bursts in 2000 it will be Gore who gets the blame. That's not a good scenario for Al Jr. to win in November of that year.