The only way Frist can lose is if he compromises and backs down.
But he won't be the one compromising. The "moderate" Senators would force the compromise on the Senate by voting for cloture. Thus, use of the nuclear option would never come up. Moreover, the moderates would vote together on the nominations to be scrapped so that that nominee did not enjoy majority support. As a consequence, invoking the constitutional option would be useless, again, not Frist's fault. Either way, he wins.