You'd need a whole host of things.
1) Monica Lewinsky is never transferred to the White House. That butterflies the GOP's doomed crusade on that issue.
2) GOP gains +5 in 1996 rather than losing 5.
3) Gingrich handles the government shutdown better, and the GOP wins the PR war.
4) Trent Lott does not give Clinton a 4th shot at signing PRWOR (welfare reform). Clinton still wins with a slightly reduced majority, but he's down to NAFTA, negotiated by his predecessor, as the grand centrist gesture of his presidency.
5) Gingrich stays in better touch with his backbench. Only a last minute betrayal by one of the plotters prevented his ouster in 1997. This way they have less incentive to be bitchy, since Gingrich saw himself as a French prime minister in cohabitation, with all the attendant consequences of that.
By the end, they're primed to pick up 15-20 seats in the House in 1998, and Gingrich stays. IIRC there are internal term limits for both Speakers and committee chairmen, so Gingrich would have to step down before Bush does.