Hmmm..."willing to bulsh*t" is too strong a term...I'd rather say able to hand the retail side of politics, sell himself and his policies to the largest audience. This doesn't have to be BS, just saying 'the right things' with sincerity [real or otherwise].
I think Cheney, like Rumsfield, would prefer to speak his mind, and his mind is not necessarily as TV friendly to the voters as Bush's is. For example, think he'd be a lot more conflicted over this Terri case if cornered. He does better work left unmolested.