There is no Democratic Tea Party because the Democrats are not the Republicans. The actual Tea Party have shown that they care more about fanatical purity than they do about governance - in fact, they are openly contemptuous about governance, along with expertise, tolerance, diversity, rationality, empathy (for those not in the in-group), empiricism, and everything else that anyone even vaguely liberal or center-left in the US ostensibly cares about. It's in the Tea Partiers' DNA - hell, it's in the DNA of Americans in general. Furthermore, they are driven by a fundamentalist, absolutist mindset that regards compromise as weakness and diversity of opinion as a bad thing.
The vulgar Right is antithetical to everything Democrats stand for. It would be insane and foolish of the Democrats to attempt to emulate them.
I'm not saying the Democrats should take Tea Party-like stances. I just think a Democratic Tea Party should use Tea Party-style techniques.