I am not happy with the counsel handling my DUI case. What are the odds of finding an attorney with the trial a month away?

You have the absolute right to be represented by the attorney of your choosing. Let your current attorney know that you’re not happy, and that you’re planning on changing counsel. This doesn’t have to be acrimonious. Sometimes attorney/client relationships just don’t have good chemistry, but you have a lot at stake and need to find someone that you are satisfied working with. Two qualified professionals should make the transition between attorneys relatively seamless. Its as simple as filing a notice of withdrawal and substitution with the court.