This is my best guess:
With the economy in the dumps, the economy still dominates the election, but because Ferraro is seen as being too liberal by many the election is much closer than it was in real life. Ross Perot runs slightly better in this election as well. The election isn't called for several days, as Iowa is too close to call and a recount is demanded by President Bush. In the end Ferraro wins Iowa by a few hundred votes and as a result she wins the Presidency becoming the first woman to do so.
Electoral VotesFerraro/Clinton 271
Bush/Quayle 264
Perot/Stockdale 3
Popular VoteFerraro/Clinton 40.0%
Bush/Quayle 38.5%
Perot/Stockdale 20.9%