Court Appointed Attorneys
These lawyers are paid by the state to represent poor or indigent criminal defendants. If you are assigned a court appointed attorney, you should expect the same professional representation that you would expect if you had the money to hire a private attorney. However, an expectation of adequate representation does not mean you can change your court appointed attorney if you do not "like" her. You will only be able to obtain a different attorney if you can show you are being so inadequately represented you are unable to get a fair trial.
If, during the course of the criminal proceedings against you, you are no longer indigent, your attorney is under a duty to inform the court and she may be allowed to withdraw. Alternatively, the attorney can continue to represent you under a partial payment plan that some states use in criminal cases where the defendant has some (but very limited) assets.