Could it be that Republicans would support a President from their own party (as Dems would a Pres. from their party) who had slam-dunked the 1972 election vs. Sen. George McGovern? Despite the controversy of the Vietnam War, a lot of Americans supported Nixon's presidency. He was not THAT unpopular outside of academic and media circles (and, of course, the Democratic Party).
If that doesn't convince you, do you recall the resurrected Nixon of the 1980's who was sought out for his opinions and commentary regarding the events of the day, especially foreign policy? Frankly, I was NOT a Nixon fan, but many people (including those not exactly in his corner) recognized that the man was intelligent, highly experienced and might have something of value to contribute after all. Other than the more extreme members of the Left, people generally cut Nixon a break by the 80's and he was not the despised character some expected he always would be.