Unfortunately, a public defender must be appointed by a judge. That means you cannot get a public defender until after you have already been arrested. So a public defender is of no help to you in your current situation.
However, you do not have to speak to the police at all without a lawyer. In fact, you are not required to speak to the police at all. You have a Constitutional right against self-incrimination. What that means is when you are the suspect of a crime, you NEVER have to submit to police questioning if you do not want to.
Exercising that 5th Amendment right cannot ever be used against you. Once you agree to talk to the police, however, anything you say can be twisted and used against you.
So, when the police call again, you can simply turn the detective down and tell them that until you've obtained representation, you have nothing you wish to discuss with them at this time. The police won't be happy, but they know that you have rights and will not bother you further about talking to them.
Many times when the police reach out like this, it's because they don't have enough evidence to arrest you and they are hoping you'll give it to them. So exercising your constitutional right against self-incrimination may prevent your arrest altogether. If they do have enough to arrest you, however, they will. But at least you won't have made a confession which would pretty much seal your fate by damaging your ability to fight the case.