As an executor of the estate and potential heir - you are not responsible for the debt.
You obligation as an executor to collect all assets, inform creditors, pay or negotiate debts, pay funeral expenses, file tax returns for the decedent, and distribute the rest of the estate to heirs.
As there will be nothing left - you do not need to transfer assets to your name, but distribute it to the estate. You would need to obtain the tax ID for the estate and file estate tax return as there will be taxable income. As an executor - you will be personally liable for her tax liability.
You may compensate yourself for being executor from estate funds.
Please see this publication - http://www.irs.gov/pub/irs-pdf/p559.pdf