The PODs necessary for Bush to win in 1992 with Robertson as his running mate would have to be huge, but considering that this would have happened at a time when the Religious Right was on the ascendant, it's not entirely impossible. And that's pretty fucking scary.
Of course, the Democrats would still control Congress (barring the POD that got Bush reelected), so Robertson would be able to implement a large chunk of his batshit crazy agenda. But the country would still be in big trouble.
We would likely see all gays and lesbians fired from all federal agencies, as I don't think there were any laws against this at the time (if I'm wrong, someone please correct me), and there would be borderline illegal harassment of non-Christians and non-evangelical Christians within federal agencies. All federal appointees that don't require congressional approval would be filled with evangelical Christians. In any way where executive orders can be utilized, Robertson would push his hard Christian right agenda.
If Bush had been assassinated by Iraqi agents, we would clearly see massive attacks on the country, and likely a full-scale invasion.
The good news is that the people would be so horrified by what was happening that they would turn obertson out heavily in 1996, assuming, of course, that the Constitution is still in force by then.