You might be able to do this with two PoDs.
First, Perot hires some better strategists and runs a stronger campaign in 1992, winning the presidency. This boosts public interest in third parties and independents, who poll well throughout the 90s and win a few positions nationwide.
Second, as mentioned in
another front-page thread,
Timmons v. Twin Cities Area New Party goes the other way and the Supreme Court rules that the prohibition of electoral fusion is unconstitutional, further strengthening third parties.
Eventually under these conditions Ralph Nader becomes a Senator and builds a reputation as a competent and successful legislator.
During a particularly disastrous Democratic presidency (doesn't matter who - it'd be determined by the butterflies from a Perot presidency), a disaster such as the Gulf oil spill is badly mishandled. As the Dem's reelection campaign ramps up, he and his main Republican and Reform Party opponents are proved to have collected major campaign contributions from the (now exceedingly unpopular) company who caused the disaster.
The ticket of Sen. Ralph Nader (G-CT) and Rep. Jello Biafra (G-CA) wins a plurality of the popular vote in the ensuing election. Knowing that they can't hope to redeem their unpopular incumbent, the Democratic caucus in Congress votes along with Green and New Party representatives to elect the Green ticket.
Bump off Nader and there you go. I doubt Jello Biafra could ever be elected outright - he's too openly radical for that.