Most people do not owe estate taxes when they die, so they should not be a critical part of your estate planning unless you believe the total value of your estate will exceed the federal estate-tax exclusion amount -- $5.25 million, as of 2013. If the value of your assets is more than this, the burden of filing and paying estate taxes falls to the executor of your will during the probate process. If she doesn't do her job properly, the IRS can look to her for payment after your estate is closed.
Closing the Estate
Your executor cannot – or should not – settle your estate until she has filed all required tax returns. These include your personal returns, as well as an estate tax return if it is required. She has nine months from your date of death to do so. After she determines how much your estate owes in taxes, she's obligated to pay this debt first, before other creditors receive money and before making distributions to your beneficiaries. The IRS will issue a closing letter about six months after reviewing the return, allowing her to make distributions and settle your estate.
If your executor fails to file a return or neglects to pay any taxes due, she can be held personally liable. She won't necessarily have to pay all your taxes, but only an amount equal to what she gave other creditors instead, or what she distributed to beneficiaries before paying the IRS. This can occur even after your estate is settled.