No way.
The Democratic Party has pretty much adopted the slogan: All big government, all the time. And no, those petty DINOs in places like Oklahoma, Kentucky, and other places don't count since their voices don't mean jack Bo Diddley when talking with the big boys and girls.
The Democratic Party has adopted the slogan … Let's become the Diet Republican party! (The party years before George W. Bush. The Republican Party expanded government. But plenty of their defenders are brainwashed into thinking otherwise.)
Hey, I'm not denying that the Republican Party is full of hypocrisy (I am anything but a fan of the Grand Old Authoritarian Party) for advocating small government while expanding government beyond what "big goverment liberal" Democrats have. Bush did oversee the biggest expansion of government since LBJ (maybe even bigger), just saying I don't expect the Democratic Party to have an official "State's Rights" plank in their platform anytime soon (considering how many issues they want to leave up to the federal government).
With the exception of drug laws and gay marriage I can't really think of any other issues that the Democrats are like "yay! State's Rights!"