Can public attorney defend me in this case?

Shall I guess you're in California?

I have reads that the penalty can be 3 years of probation (informal) and a $1,000 fine, up to 6 months in jail, and a $1,000 fine.

If the value of the stolen property was $50 or less and you have a clean record this could be reduced to an infraction and a $250 maximum fine.

If the value is OVER $50 but it is your first offense you MAY be able to participate in a diversion program which will require community service, payment to the store for the merchandise, something of that nature.

I would not attempt to enter a plea, plead down or ask for diversion without an Attorney. The only way to know if you qualify for free legal assistance is to ask.