I recall reading somewhere, and of course I can't find it now, that many of Clinton's advisers were engaged in hand-wringing over a potential Jesse Jackson challenge in either the primaries or the general election. They were able to avoid that problem, obviously, but it seems to me like that would be a good place to start for Dole to win.
So, let's see. In mid-1995, Jackson holds a press conference and announces what everyone has been fearing for months: tired of the rightward shift of the Democratic party under the guidance of the Democrats for the Leisure Class, he will challenge president Clinton for the party's nomination. Jackson never has a lead in any of the polls nationally, but does manage to take Illinois, Michigan, and South Carolina during the race. The damage, however, is done. Many liberals are disaffected with Clinton's shift to the center, many centrists are disaffected by his pandering to the left in the primaries, many minorities are convinced to stay home rather than vote for Clinton.
Dole wraps up the primaries in a similar fashion to OTL. Buchanan makes his threat that he will break away from the party unless Dole picks a pro-life VP. Unlike OTL, though, he selects first-term senator Rick Santorum as his running-mate. Santorum's youthful energy and charisma are a balance to Dole's age and clumsiness with words, and the Republican ticket receives a poll bounce, virtually tying them with Clinton/Gore at 47% each.
Come election day, Dole/Santorum hold on to a slim 48% to 47% lead to win the race 273 to 265.