Mona Charen is correct that mainstream Democrats have used the term “states’ rights.” In fact, one of them is President Obama:
From a statement of administration policy opposing an appropriations bill: “Section 810 of the bill prevents the District of Columbia from using its own funds for abortions, which undermines the principle of states’ rights and of D.C. home rule.”
From remarks on signing a memorandum on non-discrimination: “Among the steps we have not yet taken is to repeal the Defense of Marriage Act. I believe it’s discriminatory, I think it interferes with states’ rights, and we will work with Congress to overturn it.”