The most recent DNC Bylaws I could find was from Sept. 2009. Someone let me know if Article V has been revised since then. But here is the relevant part:
Article V, Section 2(b):
"The National Chairperson shall be elected and may be removed by a majority vote of the Democratic National Committee [...]."
Just FYI.
According to this link, the DNC has 447 members, 75 of which are appointed by the chair (and would presumably be loyal to said chair).
So, unless I'm missing something, you need 224 votes from the DNC membership to remove the chair.
It is highly regrettable that it's come to this, but I just read about the "Democrats Wins Seats" PAC and that was the last straw for me.