Convicted of petty theft (misdemeanor) serving a total of 28 days in CA can it get me my deferral action application denied?

Your question requires an attorney consultation. It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated. The short answer is possibly, since it may be considered a crime of moral turpitude. I strongly suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your situation. He/she would then be in a better position to analyze your case and advise you of your options.

Yes, crimes and convictions have consequences, including denial of immigration, employment, etc.