The Minister for Children Katherine Zappone is claiming that people who look after their grandchildren would be "insulted" by the idea of receiving payments from the state.
New childcare benefits introduced in the budget can only be used to pay for registered creches.
But some, including Transport Minister Shane Ross, want the payment extended in future budgets to include grandparents and other relatives who take up child-minding duties.
In an interview in the Sunday Independent, Katherine Zappone said the benefit would take the pressure of child-minding off family members.
She also ruled out payments for stay-at-home parents.