The core Democratic values of fairness, opportunity, and investing in our nation and people very much speak to the concept of personal liberties -- an open society where success is predicated on the merit of our ideas and efforts, unduly burdened by the government, corporate America, or other individuals. And rather than always get in the way, government can facilitate this.
Of course, this also means that government isn't always the solution to the nation's problems. There are times when business-government partnerships can be extremely effective (such as job retraining efforts for displaced workers). There are times when government really should butt out (like a great deal of small-business regulation). Our first proposed solution to a problem facing our nation shouldn't be more regulation, more government programs, more bureaucracy.
The key here isn't universal liberty from government intrusion, but policies that maximize individual freedom, and who can protect those individual freedoms best from those who would infringe.
I'm not sure if I buy it, but if there's one Libertarian Democrat it's probably a bigger movement than Little Green Footballs Libertarianism. (See #9, #23, #37, and #108.)