Sen. McCain:
First, I'd like to express my gratitude and humility at being asked to serve as your running mate. It's quite an honor. I must admit, I was quite surprised when I got your call this morning. After all, I'm a strong supporter of your opponent, and you and I have very little in common as far as policy goes. I realize I'm not the first person you have offered this position to, and you're probably starting to feel a bit desperate, but even so, wow, what an honor!
It is with a mixture of regret, admiration, and schadenfreude that, after careful (albeit very brief) consideration, I must decline your remarkable offer. After all, I can't in good conscience endorse someone who I believe to be a terrible fit for the office to which you aspire, and I can't bring myself to run alongside someone I simply cannot support. Thank you anyway, and best of luck in your future endeavors in the US Senate.
Update: Please don't beg, John. It's unbecoming. Although I must admit I was tempted by your offer to sweeten the deal by offering me one of your spare houses...