A sole parent with two children on $55,000 would also be more than $20,000 worse off over four years — or up to $6,000 a year.
Labor's families spokeswoman, Jenny Macklin, said the figures showed the budget was grossly unfair and would hit hundreds of thousands of low and middle-income families.
"The message from these figures is that the only way to protect these families is to reject these cuts in the Senate when the Government next presents them," Ms Macklin told AM.
The modelling shows the lowest income families would lose about 7 per cent of their disposable income, whereas the richest families would have a tiny gain.
Parliamentary secretary to the prime minister Christian Porter told Sky those measures would fund a proposed increase to child care.
"The fiscal reality is that there must be savings that you garner to pay for the package," Mr Porter said.
"I think that might just focus the mind of crossbenchers.
"Because if they go back to their constituencies who want the benefits of the childcare package, and who I think ultimately will be willing to live with savings in other areas, that ultimately will put pressure on the crossbenchers that maybe hasn't been there before."
Ms Macklin said asking families to accept the trade-off was unfair.
"The Government should not be saying to families that face a cut to their income of more than $6,000 a year that they have to take that cut for other families to get improvements to child care," she said.
"That is just outrageously unfair and families are very, very angry that that is the way that Tony Abbott is treating them."