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It is common to think that while Harold Stassen's candidacy for the Republican nomination for the presidency in 1948 was serious, he had no chance thereafter of winning the White House. (His 1952 hope that a GOP convention deadlocked betwen Eisenhower and Taft would turn to him was pretty forlorn.) I would like to suggest one way it could have happened:

Stassen (who had been President of the University of Pennsylvania in 1948-53) ran for the governorship of Pennsylvania in 1958, but lost the GOP primary to Albert McGonigle, 54.52%-32.44%. http://www.ourcampaigns.com/RaceDetail.html?RaceID=43864 McGonigle went on to narrowly lose the general election to Pittsburgh mayor David L. Lawrence. http://www.ourcampaigns.com/RaceDetail.html?RaceID=41298 This was not a bad showing for a Republican in the Democratic year of 1958, and in that same year Republican Hugh Scott defeated Democrat George Leader for the US Senate. Given the relatively strong showing by the Pennsylvania GOP in statewide races in 1958, it is not inconceivable that if Stassen had gotten the gubernatorial nomination he could have won the general election and maybe even again be talked about seriously for a GOP national ticket. Nixon (who had backed Stassen for the presidency in 1948) would certainly like a running mate who could help him in *both* Minnesota and Pennsylvania, both of which were closely contested in 1960. http://psephos.adam-carr.net/countries/u/usa/pres/1960.txt (Stassen might help in other closely contested states as well. Having become a Philadelphian, he might attract voters just across the river in New Jersey.)

Of course the problem is that Stassen had committed the blunder of urging the GOP to dump Nixon in 1956. If he had avoided that mistake, maybe Pennsylvania GOP leaders would look more kindly on his 1958 gubernatorial candidacy, and as noted, if he got the GOP nomination he had a reasonable chance of defeating Lawrence. Or another way Stassen could win: Maybe Philadelphia Mayor Richardson Dilworth gets the Democratic nomination and *then* makes the mistake of giving a "soft" answer to a question about the admission of Communist China to the UN. (In OTL, Dilworth made that mistake *before* the nomination for governor was decided on, and it provided a reason--or at least an excuse--for the bosses to deny him the nomination.) Let me add that I personally admire Dilworth, and that he showed admirable courage as a passenger on the *Andrea Doria.* But he proved a very bad campaigner for governor against William Scranton in 1962, and might have also done so against Stassen in 1958. The joke was that Dilworth was "born with a silver foot in his mouth." https://books.google.com/books?id=6SpJJmkNDFEC&pg=PA197

So Nixon/Stassen wins in 1960 (given the closeness of the OTL election and the help that Stassen might bring to the ticket in some close states, this is plausible). If Nixon serves two terms, Stassen might be Nixon's successor in 1968 (he will only be 61 then). Or an assassin could make him president a few years earlier...
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