Well, the big thing to take into account is looking at what his policies and choices would've done. George HW Bush probably would not have implemented what Bill Clinton did to try and fix the economy. This means a longer weak economy as a result of the infamous "voodoo economics." Granted, it all depends on what he would do. If he increased the taxes like he did last time, it would further encourage hard-liners on his side while committing to not doing so would just basically leave the economy weaker for a longer period of time.
Another thing to consider would be the Whitewater controversy and how that would affect the Clintons' standing with the Dems. I'm not sure as how big a deal it would've been; I mean, he was a presidental candidate, but not currently the president. Depending on how things go, it could probably the Dems to further seperate themselves from him if things got bad enough. Though this leaves an opening for 1996. One possible scenario would be the Democrats going for a further left candidate to try and counter the Republicans, who would probably be struggling by this point, either from Bush doing the tax thing again or doing so and being blamed for the economy.
This is my inexperience and lack of knowledge talking, but maybe the Dems would be willing to back Nader up as their candidate. James D. Griffin is hard to tell though he might compromise on economic issues with the Dems as long as he opts out of much with societal issues, though he may be too conservative for them to be a serious presidential candidate. LaRouche would probably also be a dud if due to the past controversies associated with him in the past. Al Gore seems to be the most likely one and he could his prior experience to help. He'd probably do something akin to the Clinton tax reforms and probably sneak in some of his green energy policies there.
Though this leaves Al Gore in how to handle 9/11 though... he'd be an incumbent if he was re-elected and if the Neocons aren't in much position, there could be a quicker capture to Bin Laden if the focus was on Afhganistan instead of Iraq, but I don't know that much on this. It would definitely give a large deal of support and help the Dems out as well. If Bin Laden was captured on in his tenure, he'd leave a pretty accomplished president and this leaves whoever would get would follow him some big shoes to fill.
Now, assuming this is all what happens (for all I know, the Dems could win Nader over and he could win. Reality likes to defy expectations), then it's 2004. Let's say Bin Laden was captured and such, this leaves the nation in a state of what-now. Granted, there are still corporate scandals and economic things to face. Whoever would be in 2004 would have to deal with Katrina (which would make for a hilarious call-back to Gore's mentions of climate change).
The economy is complicated given how it tends to be caused whenever people and corporations go overboard on things (like 2001, the dotcom bubble burst and in 2008, on housing.) Whether it would happen here... I have no idea. It could happen because of the tide of good feelings from Gore's presidency, but his
economic policies does seem to have him be the cautious type. He might raise taxes on the rich and try at least put a carbon tax, which could help. Whether what he would put it in would deal with the housing crisis... I don't know.
Let's say the GOP ends up winning the 2004 election. Whoever they put in would have to deal with Katrina and that would affect things. If things remain the same regarding the Housing crisis (I am very unsure if it would, but let's say it does), the GOP would take a blame for it. If it was delayed a bit to where they still won in 2008 and it happened there... not fun for them. 2012-2020 may go to the Dems if the GOP botch it up there.