While not wholly responsible for the Bush win, the tape certanly helped.
Actually, a survey done after the tape (posted somewhere here on FR) said that most voters who claimed they had been influenced by the tape had decided to vote for Kerry, because they thought he could "negotiate" with Binnie.
My first thought when I saw the tape and the relatively conciliatory tone of Binnie was that it was going to assure a Kerry win, because he was offering the sham Islamic truce (hudna) if Bush was not elected.
The press tried to censor it because they didn't want it to look as if Binnie supported their boy, but the threats to the "states" (as in US states, not nations) that supported Bush came out in time to make it clear that Binnie was supporting Kerry.
I think it was a wash. Cowards still voted for Kerry, and people who were PO'd still voted for Bush.
The other side of the coin is that with all our effort and billions of dollars put into getting Bin Laden, he is still out there and lecturing us. Some would interpret that as maybe we need a new Sheriff. Tom.