The answer is: possibly. The rules for withdrawing a plea are set out in Cal. Penal Code 1018, which state that before judgment or within six months of being placed on probation, the court may permit a withdrawal if the defendant who is able to show "good cause." Unlike most things in the criminal court system, you will have the burden of showing with clear and convicing evidence that you have good cause.
You should consult an attorney as soon as possible [particularly given your time issues] to preserve your right to withdrawal. A competent attorney should be able to look at your case and advise you first, about why you may or may not wish to withdraw your plea and second, if you have good cause.
The first thing you should do is look at the documents your attorney gave you...specifically the retainer agreement and see if there's anything in there about a conflict.
Also, due to the time-sensitive nature of the plea withdrawal, you should hire an experienced criminal law attorney to get started on the process for you ASAP.