Assuming you can claim Head of Household with two children, your standard deduction would be $9,250 and 3 exemption at $4,000 each would be $12,000. So nothing would be taxed under the total of $21,250. Also you might qualify for a $2,000 child tax credit for the two children. You probably qualify for an EIC (Earned Income Credit) to boot. So zero withholding seems appropriate.
**Disclaimer: This post is for discussion purposes only and is NOT tax advice. The author takes no responsibility for the accuracy of any information in this post.**