Legal Question in Criminal Law in California

The judge isn't going to keep continuing your case forever for you to never get a lawyer. Sooner or later you are going to end up with either the public defender or in a situation where you are proceeding without a lawyer. You need to figure out which is which and get moving.

Yes, most judges will allow you time (within reason) to find an attorney. If you keep finding that you can't afford one, you can always request a public defender. If you're in that grey area where you earn too much to qualify for a public defender, but you don't have enough to hire an attorney, the court may have a panel of attorneys that agree to take cases for a lower fee when referred by the court.

You can ask. Its not clear from your question how many times you have already asked the question but if its only once or maybe twice the judge should grant you time. Another place you may look for a low cost attorney is the county bar association which may screen clients for a low fee attorney panel. If the judge insists upon appointing the public defender you may continue looking for an attorney and when you find one you can substitute the attorney for the public defender.