Cuccinelli of VA and McCollum of FL are both under that impression. I've heard each of them on several occasions state that if SCOTUS finds just on part of ObamaCare unconstitutional, then the *entire* law goes down because of its lack of a severability clause.
"[A] court should refrain from invalidating more of the statute than is necessary. . . . [W]henever an act of Congress contains unobjectionable provisions separable from those found to be unconstitutional, it is the duty of this court to so declare, and to maintain the act in so far as it is valid." Alaska Airlines, Inc. v. Brock.
"[W]e try not to nullify more of a legislatures work than is necessary, for we know that [a] ruling of unconstitutionality frustrates the intent of the elected representatives of the people." Ayotte v. Planned Parenthood of N. New Eng.