The standard-bearers of that latter ethos often try to dissociate themselves and the national party from figures like Michele Bachmann and Steve King -- people whose differences with the pro-donor wing of the party are both rhetorical and substantive.
The party's differences with Liz Cheney, by contrast, are purely stylistic. Senator Cheney probably wouldn't spend too much of her time trying to de-fluoridate the water supply, and would be a great ally to the conservative economic and fiscal mainstream. She'd actually be a triumph of political engineering if there were a huge constituency for draping policies that benefit the rich in dÃ©classÃ© rhetorical extremism. But that constituency is very small and unpopular, almost by definition. And simply by engaging in a particular approach to politics the party wants to inch away from -- slowly, gently, without alienating its base -- she'll make the task of dialing it down a notch very difficult.
Which is a big reason, I think, why professional Republicans are scared of her candidacy.