To give Perot any chance of winning outright, you would need to seriously derail the general election campaigns of both Bush and Clinton. Fortunately, the nature of each party's 1992 primary season creates something of an opening.
Folks forget this, but Jerry Brown had strong showings in several primaries during the later stages of the Democratic primary season before losing some steam due to gaffes. Here, have him avoid said gaffes and continue his momentum all the way to the DNC, with several commentators describing him as essentially the presumptive nominee. However, due to Clinton's early primary wins, nobody goes into the convention with a majority of delegates. In what is widely derided as an unfair backroom deal after the fact, Clinton is able to marshal just enough support with the party establishment to win the nomination. An outraged Brown, encouraged by his supporters and even those who were previously neutral, decides to cast his lot with Perot and join the independent ticket as a running mate. This means that Perot does not merely have a prominent running mate, but one widely considered to be the rightful Democratic presidential nominee. Tsongas, who was equally sympathetic to Perot beforehand and disgusted by the choice of Clinton, openly endorses and campaigns for the Perot/Brown ticket. Clinton is initially able to retain the support of most Democrats with a more conventional choice of running mate than Gore, perhaps a northeastern liberal such as Bradley or Cuomo, but then a massive sex scandal surfaces at some point in the general election. Maybe Juanita Broaddrick, after seeing all of the negative media attention that Clinton receives in the aftermath of the DNC, is more willing to publicly accuse him of rape during the general election campaign. Clinton never recovers - perhaps the party even replaces him on the ticket with another candidate late in the game, but that just creates more chaos that does not allow the new candidate to gain much traction.
On the Republican side, Pat Buchanan narrowly defeats Bush in the New Hampshire primary, which gives him the momentum necessary to seriously contest other early primaries. Bush still ultimately wins, of course, but the fact that Buchanan won anything against a sitting president at all convinces his team that he needs to shore up his support among cultural conservatives. Dan Quayle makes some sort of serious gaffe (which is certainly not implausible) which creates the perfect opportunity for the Bush campaign to replace him on the ticket with someone like Jesse Helms, who gives a speech at the RNC that makes Buchanan's OTL convention speech look like it was written by Ted Kennedy in comparison. Buchanan himself, though, sulks over what he perceives as dirty tricks employed by Bush to smear him and derail his campaign. Already sympathetic to Perot's position on trade, Buchanan is conspicuously absent from the RNC and, while he may or may not openly endorse Perot, he certainly does make some very positive public statements about the man. Thus, Bush gets all the blow-back from moderates one would expect from picking a person like Helms to be his running mate without even improving his standing very much among Buchanan voters.
Throw in a serious scandal for Bush as well as Clinton during the general election, and Perot may have a real chance to win the election outright.
