In a way yes but I just feel a 'stepping stone' has been removed from this argument. I regard the primary responsibilities of being a parent as ensuring that their children are fed,clothed and sheltered. Should they not be in a position to adequately provide these three umbrellas over them then there has to be sufficient financial services from the government that they can apply for and claim to cover any shortfall they are experiencing.
The difficulty then is ensuring that the money does go to the direct benefit of the child and is not mispent by irresponsible parents on frivolous items, but you should not remove that duty/responsibility from the parents and try to place it upon the shoulders of the government.
So my answer to your question would be : It is the responsibility of the government to see that services and financial support is available to parents who cannot provide their children with the basics of survival : food, clothing and shelter.