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All recent presidents were tarred with illegitimacy: Clinton never won a majority, only pluralities, and was impeached; Democrats viewed both Bush elections as stolen; birtherism was an attempt to delegitimate Obama, and you can add to that the "Chicago politician"/ACORN stuff.
Of course, there's the current guy with the Manchurian candidate narrative that emerged right after his election; and the likely next guy will be seen as having stolen the election by a decent portion of the country. Two thoughts on this:
An obvious takeaway is that as the country settled into ~50/50 polarization where it was taken for granted the vast majority of votes weren't even up for grabs, one result was a War of the Roses-like logic where you can only have legitimate heirs or pretenders.
Less obviously, I suspect there's a Laschian culture of narcissism analysis to be done here. As sense of self becomes more linked to political affiliation, the prospect of loss or failure of one's one side is too self-wounding to recognize, and is fended off via projection.
If your party and its standard bearer have become a locus of ego-identification, to acknowledge "the people" rejected it/him is felt as a devastating judgment on you. Rather than accept this, you must project that dreaded negativity onto the Other in the form of illegitimacy."
