This must be weighed against the proportion of the audience in whom such a phrase would inspire exactly the opposite reaction (or, more likely, a stronger but opposite one). Though it's not the phase itself but the associations the phrase triggers that'd do the damage; few people want to be unthinking adherents of anything but many have heard phrases like "unthinking and unquestioning" used to describe their political allies.

No idea what those proportions would be here, though.