"write off" when used like this is functionally equivalent to "dismiss", i.e. to stop caring about it. "write off" it comes from the financial world, usually about taxes. a "write-off" is something that you claim as a "business expense", (or some other kind of expense which does not require taxes paid), so you don't have to pay taxes on it.
the sentence is not very clear: I will add some marks to help you separate the parts:
That was on Wednesday, November 20, 1963, the second of his last two full days in Washington.
Anyone [(who is) under the impression that the President of the United States was devoting his full energy to wardrobes and coiffures] is invited to examine his (the President's) activity during those final White House hours. (意譯：Anyone who thinks that the present is only thinking about clothing or hairstyle should see what he does during those final hours)
Monday had been a day of formal speeches and informal politicking in Florida (another ten electoral votes that couldn't be written off [we need those 10 votes, and we are unsure we will win them]), and Tuesday he had reached the office early. 】