The Federal Government says it is willing to further compromise with the Senate crossbench in order to pass the remainder of its planned changes to family tax benefits.

The Senate last night passed a bill to scrap Family Tax Benefit (FTB) Part B for couples, once their youngest child turns 13.

The current age limit is 18 for those teenagers who finish high school, and 16 for those who do not.

Labor supported the bill, but opposes the remainder of the Government's plan.

Nonetheless, Social Services Minister Christian Porter will reintroduce over $4 billion of other savings to Parliament on Wednesday, and is looking to the crossbench for support.

"We're in the art of the possible here," Mr Porter told AM.

"I'd rather have a save compromised but actually have a prospect of passing through Parliament, which means we actually get reforms to child care, than be doctrinaire about it all and be unwilling to compromise, so compromise it is."

The Government will lose about $70 million in savings by exempting grandparent and great-grandparent carers, and single parents over the age of 60 from changes to FTB Part B.

Mr Porter said those exemptions were being proposed after initial discussions with some senators.

"In my conversations with the crossbench, I've not put the heavy on and tried to get an answer 'yes or no' right now," Mr Porter told AM.

"But I've listened and engaged and tried to work out what ways we can modify things, and other things we've got on our books to try and secure passage through the Senate."

Call for other kinship carers to be included in revised legislation

The bulk of the proposed savings come from phasing out supplement payments to family tax benefit recipients, which the Minister argued were no longer needed.

"These payments were meant to allow people to pay off debts that were being occasioned back in 2004 when we were in massive surplus," Mr Porter said.

"Debts have stabilised and we are now paying money, in circumstances where we are in deficit, to families, to pay debts which, overwhelmingly, they no longer accrue."

But Labor's spokeswoman for communities and carers, Claire Moore, told the Senate that the additional payments were crucial to low income families' budgets.

"These amounts of money actually make a real difference in the survival budgets of people raising children," Senator Moore said.

The Greens have also opposed the changes, and have said they will not be voting for the revised legislation.

Spokeswoman Rachel Siewert told the Senate that the Government should also exclude other family-based carers from the proposed changes.

"While I'm really pleased that they're finally paying attention to grandparent carers — because for so long they have ignored them — they now seem to forget there's kinship carers, foster carers, but in particular kinship carers," she said.

"Grandparent carers are actually fewer in number than other kinship carers."

Mr Porter told AM it had not been raised with him before, but he would consider Senator Siewert's concerns.

"I'm not sure how many people identify as kinship carers, or indeed whether there's a good measure of formally identifying through the system. I'm happy to look at any suggestion," he said.