Liberal Democrat John Thurso said some of the poorest families suffered "misery and hardship" because they were being asked to pay back thousands of pounds awarded to them in error.
He highlighted the sheer volume of errors made by the Inland Revenue and said the complexity of the system meant it was easy for claimants to make honest mistakes. "The system should be a lifeline, not a torpedo," he added.
Labour member David Taylor suggested the right to recover overpayments resulting from official error should be ended and there ought to be "statutory tests for recoverability".
But John Healey, economic secretary to the Treasury, said: "An amnesty across the board is not an appropriate way of dealing with overpayments." He said the Inland Revenue was streamlining its procedures for dealing with overpayments. A backlog of cases should be more than halved by the summer.