WE sold my dad's house from his estate. At the time of his death the house was appraised at a much higher price than we could reçeive today. Do the heirs have to pay income tax on their portion they rec'd?

No. I assume that your father passed away in 2009 or earlier - correct? If so, then your tax cost basis in the property is equal too the fair market value of the home as of his date of death. If you sell the house for more than that amount, you would owe capital gains tax on the gain over the cost basis. But if you sell for less than that amount, the loss is not deductible (losses on personal property are not deductible). So in this case there is nothing to report with respect to income taxes,