The Untited States Presidential Election that occured in November, 1994 featured the Repulican incumbent against a likely democratic challenger. Based on the Democrats' continued control of the House and Senate, it seems likely that this election did not feature strong coattails on behalf of the Republican ticket. It can be presumed that whatever candidate and winner of the vice presidency was also the Republican nominee for President in 1998.
In a conversation between Josh Lyman and Sam Seaborn in Season 7 of The West Wing, it is mentioned that the last time the Democrats had controlled the House had been 8 years before, indicating that the Democrats must have controlled at least 1/2 of Congress by this general, or midterm election.