That is not what "conflict" means. A conflict exists where the public defender's office represents two defendants with different interests. You do not have this. What you have a disagreement with you attorney about how best to handle the case. In a sense both you and PD are right. The law gives you the final decision whether to plead guilty or to go to trial, and if you insist on a trial then the PD must accept your decision. But your lawyer, be it a PD or a private attorney, has a duty and obligation to level with you and to tell you the truth, and if the PD on the basis of her experience and her review of the evidence believes that a trial would end in your conviction then it is her duty to tell you so, and if you have any sense you will listen to her, which does not mean that you will accept her advice; it means that you will listen seriously to what she has to say and not blow it off the way you are doing. She is trying to help you by keeping you from making a mistake that could result in a much stiffer punishment than you might otherwise get. You do not want a lawyer who tells you what you want to hear. But by all means, pay for a second opinion. Take a copy of your file to a private attorney and ask for an evaluation.
If you were my retained client I would give you the straight dope on what I thought would happen if your case went to trial. I would absolutely not "give you the benefit of the doubt," whatever that is supposed to mean. If I thought you would be convicted, I would tell you so. If I thought that your conviction would result in a longer sentence on a more serious charge than I could get for you on a plea, I would tell you so. And then if you told me, "Damn the torpedoes! Full speed ahead!" then we would try the case and hope for the best, but at least you would have your eyes open. It sounds like that is what your PD is doing. I don't see that you have anything to complain about.
A "conflict" attorney is generally appointed in cases where the Public Defender's office represents or has previously represented more than one party involved in a criminal case. You can certainly request a hearing in front of the judge and express your concerns, but I would not expect much to come of it.
You can have your Public Defender file a motion to address your concerns to the judge. The judge may appoint conflict counsel, but most often will just give you the opportunity to represent yourself, which is not recommended.
I agree with Ms. Sticco, you are likely going to be unsuccessful before your judge given the situation.
It appears the "conflict" you are referencing occurs when the public defender previously represented a victim in the case, currently represents a co-defendant, etc. It does not sound like this occurred in your case.
As a former public defender, I strongly recommend scheduling a meeting with your public defender. Public defenders are more able to address your concerns about the case during a meeting, rather than quickly during or after court.
Good luck with your case.
This answer does not, nor is it intended to, create an attorney-client relationship or constitute attorney advertising. Rather, it is offered solely for informational purposes. The facts of each case are different and unique, it is critical to consult with qualified counsel with whom information can be shared and assessed under attorney-client privilege, so that competent and quality advice can be obtained on which you can make informed decisions
You will not get a "conflict attorney" based on your question. You should request a meeting with your Public Defender and calmly and politely ask them to explain to you why they do not feel like you have a good trial case. You will likely learn that they are looking out for your best interest.