Calls for the Minister for Social, Community and Family Affairs, Mr Brennan, to delay reclaiming welfare payments it paid out in error last week were made yesterday by social groups and Opposition politicians.
Some 47,000 older people, lone parents and carers will not receive their welfare benefits today because they were mistakenly paid twice the normal rate last week.
As appeals were made to delay recouping the payments, a spokeswoman for Mr Brennan said there would be no change in the decision but the Department would continue to monitor the situation.
She said the error affected customers who received their payments by Electronic Fund Transfer directly to their bank account on Thursdays. All other customers received theirs.
Mr David Stanton TD, of Fine Gael, said more notice should have been given to those involved and it should be possible to spread the clawback over a longer period at some future date.
"It won't break the Exchequer if this clawback is delayed, however it could cause severe financial hardship to the recipients who will not receive their payments this week," he said.
The chief executive of the Carers Association, Mr Enda Egan, said the Department should have considered a more phased recouping of the money.
"We believe that the Department is handling the issue in a harsh and insensitive manner," he said.
The association had received a huge volume of calls to the National Carer Line on the issue.
The Department could give recipients a period of grace and recoup the money in a number of weeks or it could deduct the overpayment from the planned increase in the respite payment given to carers later in the year.
Alternatively the Department could give carers an option as to how they would repay it, he said.
Mr Paul Murray, of Age Action Ireland, said there was anger at the way the mistake had been dealt with in such a pre-emptory and cavalier way.
The group had received calls from people who were angry at the way the letter was sent and the lack of notice.
Mr Murray said they could have given notice of the repayment in three or six months' time.
The Labour Party's Mr Willie Penrose TD called for a review of the procedures involved in social welfare payments to ensure the situation did not arise again.
"I call on the Minister for Social and Family Affairs to instigate a review of procedures in the payment of social welfare to ensure that this kind of error does not happen again," Mr Penrose said.
One-parent family group One Family also called on the Minister to delay the process of reclaiming overpayments.
Ms Anne Bowen said: "We would urge that the Department issue a notice that the overpayment will be reclaimed perhaps in a number of weeks."