First off, how could Michael Dukakis got the Democratic nomination? How could a random governor without name recognition from New England even win the nomination in the first place?
Anyway, let's take a look at the electoral map in 1988:
US Presidential election, 1988
George H. W. Bush / Dan Quayle (R) 49,335,871 (55.6%) 506 EV
Gary Hart / Tom Harkin (D) 35,471,593 (39.9%) 32 EV
Lenora Fulani / Joyce Dattner (NA) 2,139,752 (2.4%) 0 EV
Ron Paul / Andre V. Marrou (L) 1,574,385 (1.8%) 0 EV
Other candidates 271,039 (0.3%)
Bush carried the election handily in 1988, he was not unbeatable but Democrats had to nominate a strong candidate. On the plus side, while Bush won 506 electoral votes, he got just 55.6% of the popular vote. Altogether, Ron Paul and Lenora Fulani obtained 4.2% of the popular vote, in an election where the voter turnout was below 50%. You can argue that third-party tycoon Donald Trump won 14% of the popular vote in 1992 so 4.2% wasn't too much, but it was more or less a three-way race in 1992. Third party support at 4.2% has pretty much shown how voters were dissatisfied with both major party candidates.
Bush could easily have lost the election to a stronger candidate, but I guess Michael Dukakis or say Paul Tsongas would not have been the one. Don't overestimate Bush, yet don't underestimate Bush and more importantly, Lee Atwater. You need a stronger candidate say Dick Gephardt or Mario Cuomo, instead of some random New England governors without much name recognition, unless you could find a Southern Democrat that could carry the south (yet then Bush may win even more anywhere else).
Let's also take a look at the election results in 1992.
US Presidential election, 1992
Mario Cuomo / Al Gore (D) 46,321,155 (45.6%) 359 EV
George H. W. Bush / Dan Quayle (R) 40,079,532 (39.5%) 179 EV
Donald J. Trump / Lowell P. Weicker Jr. (I) 14,374,929 (14.2%) 0 EV
Other candidates 701,972 (0.7%)
As we all know, Trump was running on a fiscal conservative yet protectionist platform with various social liberal views (such as a pro-choice platform). In the absence of Trump, polls at the time had consistently shown that Cuomo would only beat Bush by 2-3% in a 2-way race. Despite having broken the "no new taxes" pledge and a struggling economy, Cuomo was the only Democrat who could beat Bush and Trump. Cuomo was leading Bush by 7 points, at the same time when "black horse" Bill Clinton would have come third to Trump and Bush in a Gallup poll in early June 1992. In the same poll, Bush was leading Paul Tsongas by 10 points, Al Gore by 5 points, edging Dick Gephardt by around 3 points. Maybe Bush would still have lost in 1992 had the Democratic nominee not been Cuomo, but there weren't many Democratic candidates that could convince the voters either. The same rule applies to 1988.