Meanwhile, Assistant Treasurer Josh Frydenberg told Sky News that his wife, Amie, a workplace lawyer at a top Melbourne firm, had claimed two lots of payments as recently as last year.
"We accessed both schemes, as my wife was entitled to, and there are many people, I'm sure, on both sides of the House who have done that," he said.
The pair signalled a dramatic shift in tone and language from just days earlier, when various ministers - speaking on the eve of Tuesday's federal Budget - defended the axing of women's eligibility to draw on the Government's scheme if they could also claim payments from their own employers.
Cormann himself described the move, announced on Mother's Day, as a "fairness measure", saying: "If you get access already to a very generous paid parental leave scheme, there is no reason why you should be able to double-dip."
The Social Services Minister, Scott Morrison, went further, claiming that new mothers who benefited from both schemes were committing a "rort", while Hockey agreed with an interviewer who asked him if that constituted "basically fraud".
The row has overshadowed the generally positive reception to Hockey's second Budget, which included tax perks for small businesses and a A$3.5 billion ($3.7 billion) childcare package.
The abolition of "double dipping", expected to save A$1 billion over four years, was aimed primarily at public servant parents who had "two goes at the taxpayer", as Abbott put it.
Not only could they claim up to A$11,500 over 18 weeks, equivalent to the minimum wage, from the government scheme, but an executive-level public servant could receive a further A$23,500 over 14 weeks under their employment agreement.
However, 40 per cent of the estimated 80,000 women who will be affected by the move work in the private sector.
Critics pointed out that - as underlined by Cormann and Frydenberg - claiming twice was actually legal.
The opposition leader, Bill Shorten, accused the Government of insulting working women and "demonising" them as "villains".
Shorten also said that the 18-week scheme, which Labor introduced, was intended as a basic benefit for employers to build on.
The Government was also attacked from within its own ranks. The Communications Minister, Malcolm Turnbull, who has turned subtle criticism of Abbott and his Cabinet colleagues into a fine art, said that while he backed the policy, "I'm not using that language and I don't agree [with it]."
The influential Liberal Party Senator Arthur Sinodinos said it was "not a good look to be having a go at the young mothers or new mothers of Australia", adding: "I think some of the language has been a bit unfortunate. We could be a bit more empathetic."
Critics also pointed to the gulf between the new policy and the hugely generous parental leave scheme which Abbott championed for years before being forced to abandon it by colleagues last year.
