Aside from my general belief that the concept of the political center has become mostly meaningless in recent years, to the extent that there's any basis for it does anyone, including Joe Lieberman, really believe that "both parties are in danger of abandoning the political center."
I have a hard time even coming up with fantasy proposals which would reflect some crazy run-to-the-left action by the Democrats. Is Dennis Kucinich going to propose disbanding the army? Are marginal tax rates going to be raised to Eisenhower-era levels? It's difficult to imagine that anything other than a move towards Clinton-era status quo on most issues is on the table.
Lieberman's a lying politician, so the fact that he continues to lie to paint himself as the savior of the country is no surprise, but nobody else who expects to be taken seriously should help him propagate these myths.