Do Public Defenders have a duty of due process to their clients?

and if they breech that duty by legal malpractice can you sue them in the United States District Court for violating the clients 14th amendment of the bill of rights?

Public defenders must see that their clients obtain due process from the courts, they do not have a duty of due process themselves.

If you are claiming a Constitutional issue, then you can sue in federal court. The public defender must be a government employee. You may have an easier time suing for malpractice in a state court.

I doubt any suit against a public defender will go very far.

We live in a sue happy society, so you can sue anybody.

The problem is trying to find a lawyer who will work for nothing.

Public Defenders work for nothing, and what you usually get is nothing, I mean, unsatisfactory performance.

Performance is what counts in court, and nobody will extend their neck out without some greens up front (got that?)

In a capitalist society, everything works when money is the motivator.