I think the Gubernatorial elections would have gone about the same.
Democrats win control of the House by a narrow (3-5 seat) margin, electing Dick Gephardt as Speaker.
In the Senate:
Democrats gain Arkansas, Colorado, Minnesota (from Independence after Paul Wellstone's death and Dean Barkley's appointment) and New Hampshire.
Republicans gain Georgia, Missouri and New Jersey (I don't think Torricelli withdraws from the Senate race in this universe, as Democrats would be on track to gain enough Senate seats to able to hold the Senate without him).
This is probably not too far off although I think Carnahan wins in MO and maybe Allard still squeaks it out in CO (state was much more Republican then).