My Mom passed in 2010, we just received notification that she owes taxes for 2009. What do we do?

One of the responsibilities of the executor of your mother's estate is to take care of any debts she owed, including taxes. The executor will need to respond to the IRS notification, and if taxes are due pay them out of the estate's assets (as an aside - the executor should have filed an income tax return for your mother for 2010). This is why it is advisable for the executor to not distribute all the estate's assets to the heirs too soon - but rather hold some in reserve for a year or so in case old debts like this come up.

Ebaines points are well taken. While I am NOT an attorney, I DO know that the probate process in most state courts require a year to properly notify all parties of the decendet's deaths and to give them time to make a claim against the estate.

Note that if the estate has insufficient assets to pay the taxes due, neither the heirs NOR the executor are required to pay these taxes UNLESS they were distributed estate assets before the taxes were paid. If there was an early distribution, then the IRS WILL contact the heirs for payment of the taxes.