Since the children live with you, you are the only person that can claim them unless you surrendered the exemption and Child Tax Credit to the mother.
At your income, filing as Head of Household, your net income tax liability for 2011 would be -$615. In other words, you would have received a refund of $615 if NO federal income tax had been withheld from your wages for 2011. For 2012 it will be slightly larger, maybe around $650 or so.
So, take whatever has been withheld from your pay for federal income taxes and add $650 to that. That's what your refund will look like for 2012. If that's more than the $800 that you currently owe, you will receive a refund of the difference. (Don't forget that penalties and interest continue to accrue on your debt, so it may be larger than $800 now.)