Keep on John Sasso. Keep on point with a consistent message. Immediately respond to attacks, and retaliate.
He would need to do this and would need Bush to run a weaker campaign (fire Atwater maybe?) to pull off a close win. The economy was good in '88, Reagan was personally popular and his job approvals were above water by election day '88.
What if Mike Dukakis had actually won in 1988 against George H.W. Bush? Who would be in his cabinet? How would he react to the end of the Cold War and the Soviet Union. Would he win re-election in '92? and what would be very different and what wouldn't change at all?
Well for starters, the Berlin wall still would've fallen in 1989, although I see Dukakis gloating about it when it happens, so that strains relations between us and Gorbachev, and if relations get bad enough, The Soviet Union may linger on a little longer (though I don't see it surviving past the 1990s), if the Soviet Union still does collapse, it's too hard for me to say how Dukakis would respond or what he would do.
As for the Gulf War, that may or may not happen. On the one hand, Dukakis might be firm with Saddam from the start and make it clear to him that any invasion of Kuwait would have consequences instead of giving him mixed signals the was the Bush administration did OTL. I could also see things going OTL, and I could also see the invasion of Kuwait happening without a U.S. response, making the Duke look weak, or a botched war happening.
As for '92, the economy was going to go into recession regardless of who won in 1988, so if the economy goes as OTL, and Dukakis responds as bad or worse as Bush did OTL, he has an uphill battle for re election and 1992 ends up being another 1980. On the other hand, he may (and probably would) respond better to it, and if he successfully convinces people that the economy is getting better, so long as there are no foreign policy blunders, I can see him narrowly pulling it off on election day.