Why not agree to be hooked up to a lie detector ?
Because there's no such thing.
A polygraph cannot determine if something being said is a lie or not. All it does is register minute physiological changes, and those changes can be caused by any number of things. That's why polygraph results are not admissible as evidence.
The very environment they'd be in could create those changes. Just taking part in a Presidential debate could trigger a fluctuation.
Hell, if you really like steak, and I told you you were about to eat the best tasting steak you ever had,
that could cause a physiological change...