In this era of budget crises and mass lay-offs of public workers, regardless of whether refusing a case for lack of resources is ethical or not, it is being done. In San Francisco County the Public Defenders Office refuses whole categories of cases, specifically those that are going to criminal collaborative courts. Many of us contend that this practice is unethical but no court has tried to stop the PD in this practice.
Last year when the fiscal crisis was worse the PD's office refused some cases on an ad hoc basis which compounds the problem.
So are you left without counsel? The answer is a ringing NO! If you are indigent, which means you cannot pay your bills as they come due, you have a constitutional right to a free lawyer in criminal cases. In SF that means when the PD backs out the Courts appoint private counsel who will be paid by the county for their work.
Occasionally when the defendant appears to have assets (as when a defendant has bailed out) the judge will order that after the trial is over there will be a financial means hearing to determine if the defendant to repay the county for the costs of their defense. After all most people who are truly indigent cannot afford any bail.