What it says on the tin. OTL there was widespread speculation that the Kennedy campaign employed voter fraud to win the election, particularly in Illinois (note: I am not saying that the Kenendy campaign did commit voter fraud, just that that was a widely held belief in the Republican Party). Many GOP officials encouraged Nixon to contest the results and deman a recount, but Nixon declined and conceded the election.
But what if he hadn't? Say Nixon, for whatever reason (a fit of pique, someone talking to him at the right time, whatever) decides to double down and deman a recount/contest the election? If the results go his way, how does this affect his Presidency? If Kenendy comed out the winner, how does this affect Nixon's time in the wilderness?