Tánaiste Eamon Gilmore has dismissed any suggestion of rolling back on any of the cuts announced in the Budget.
Mr Gilmore said it was a very difficult and very hard budget, but said it was necessary.
The Tánaiste said the budget was a package which stands and said the government does not propose to unravel any part of it.
Meanwhile, Taoiseach Enda Kenny has defended what he described as the "toughest Budget of this administration".
Despite concerns about some Labour backbenchers, Mr Kenny said the Budget would be passed.
"Budget 2013 puts us in a position where we can measure up," he added.
"It is time for courage and conviction in order to get the right changes."
He said the Budget changes were required to ensure Ireland exited the bailout programme.
Barnardos Chief Executive has said that he thinks there is scope for the Government to make adjustments to the changes it announced to the child benefit scheme.
Speaking on RTÉ News, Fergus Finlay said that the time had come to reform the system so that better off families would get a little less, and that a little more support could be given to children who are being driven into consistent poverty.
He said there is a Government advisory group on the topic, whose report has been with the Minister for Social Protection since June but still has not been published.
Mr Finlay said his understanding is that it says that reform is possible, although it would not be easy due to constitutional and operational difficulties.
He said Barnardos had advocated a universal payment, which would perhaps be a more modest payment that could be topped up for all children before going back to school and for families in need throughout the year.
But he said it requires an act of political will to do that.
Mr Finlay said if it were to be done like that it could save the Exchequer money perhaps not that much, but certainly tens of millions.
Earlier, Roisin Shortall urged backbench TDs, especially those from Labour, to seek out alternative cost-cutting measures and put pressure on ministers to "recast" the Budget.
Ms Shortall said while it was not easy to make €3.5bn of adjustments, the Government had choices and unfortunately the ones they made will cause a lot of hardship to people.
"Some €500m or €600m can be achieved through fairer measures and I would strongly appeal to members of the Government to spend the next few days identifying those," she said.
Labour TD for Clare Michael McNamara this afternoon said that Labour TDs are pressing for parts of the Budget to be changed.
He said there was a lot of discussion taking place in the party because TDs returning home this evening will find it difficult to explain how money is being taken from children.
This is happening, he said, when pensioners in receipt of more than €100,000 a year only have to face a "tiny" increased burden on their incomes.
His party colleague Eric Byrne said TDs were able to convince the Education Minister to row back on DEIS schools last year, but that this Budget will be more difficult to unpick.
The Dublin South Central TD said that deputies are having an open discussion behind closed doors and the views of constituents are being conveyed to ministers.
Fine Gael backbencher Ray Butler said he too had a problem with the Child Benefit, cut particularly the higher reduction in payments for the third and fourth child.
Family carers protest in Dublin & Ennis over cuts
More than 300 full-time carers and supporters have protested outside Leinster House to demand the restoration of a cut to the Respite Care Grant.
However, Minister for Social Protection Joan Burton has insisted the reduction was necessary.
The Government announced in Wednesday's Budget that there would be a 19% cut, worth €325, to the grant.
Approximately 75,000 full-time carers will be affected by the reduction, which is expected to save the Exchequer €26m next year.
Some protesters came from as far away as Donegal.
They said they cared for elderly people who are ill and have disabilities of all ages.
They told journalists the cut deprived them of three days of annual leave.
Several opposition TDs and Senators met the protesters outside Leinster House.
Family carers from Co Clare, who were not in a position to attend the Dublin protest, also protested in Ennis.
Catherine Cox of the Carers' Association said they are still hopeful the Government would reverse the cut, despite Minister Burton's statement earlier that the measure will stand.
Ms Burton said she regrets any cuts in social welfare contained in the Budget, but insisted they were necessary.
Speaking on RTÉ’s Morning Ireland, she said her department had to make savings in line with all the others, but she had managed to reduce the amount of cuts originally envisaged.
Asked whether she thought the cut to the respite grant was fair, Ms Burton said core social weekly payments to carers and those with disabilities had been protected, and these were the really important payments.
Ms Burton said that despite the cuts, €20bn would still be spent on the social welfare budget next year.
"At this point in time, in terms of the country being able to borrow, to pay for social welfare, health and education, we have to meet the requirements of the lenders, and the requirements of the lenders are that we find savings," she added.