That implies more serious efforts than OTL at impeachment. Losing a house majority over it might convince them to tone down the emphasis on trying to play to "morality"/get socon voters. You get Dubya in 2000 still but with an actual popular vote lead over gore* with Dubya's vote losses to buchanan being countered by people voting for someone who walks the tightrope of being a man of faith while being a conservative able to speak more than one sentence without mentioning Jesus.
net effect is likely a slow motion version of OTL's post-2015 beginnings of evolution in the GOP to tone down the social conservatism a bit. OTL but with better rep numbers in house/senate 2000-on and say cut HRC's PV lead in 2016 by half and give Trump a couple of the close states. No real policy shifts imo. Maybe you get democrats remaining more like their 2000s selves than OTL, who knows.
* Not a majority because Nader and some people defecting to Buchanan.