That is an assumption.The letter would have been an albatross around his neck. Nobody is that good of a politician.
I do not think it is one that really bears out to be quite frank. I am unsure if enough people that voted for him would give a shit. The black community, the most outspoken against gays, would not have cared because Obama's race. Generally speaking, the people that would have really cared about some old letters about Obama being bi would have been from people that did not vote for Obama in the first place.
The stark reality here is that all the outrage about it would have been on the right from people that would not vote Obama under any circumstances whatsoever. Trump is actually a good example of this. Trump said a LOT of shit that would have sank any other politician. The fact was, however, none of Trump's voters gives a rats ass if he says vulgar shit in a locker room. ALL of the people that care about that asinine crap would have never voted for Trump anyway so those 'albatross' moments did not effect his vote totals at all.