How influential were those claims on people's opinions on Obama--or your boss?
Well, considering the sheer number of people out there today who think President Obama is a secret Muslim, or who think he wasn't born in the United States, or both, I'd presume that a fair number of those rumors circulating about then-Senator Obama in 2007 (when I had my internship) were fairly influential.
I'm not comfortable telling you what office I interned in, but suffice it to say that it was an influential public figure who could easily have made the news if he had wanted to.
Sci, is this becoming personal?
No, I'm illustrating the point that someone else from that era might look at the early Christians in a completely different light than you do. To them, they might not have looked like reasonable or even admirable people who had been swayed by faith; they may well have looked to the Romans like crazy people not worth the effort (until they'd already reached sufficient numbers that nothing the Romans said could ever change things, especially since the early Christians could just as easily accuse the Romans of lying as the Romans could the Christians of lying).