Children should be given equal opportunities in life regardless of their parents' decisions.  Though the mother is clearly an idiot for saying that "someone should be held accountable" (you mean yourself? idiot), the children should not have to suffer for her lack of responsibility.  If nobody is willing to support them voluntarily, then I must argue that this is one of the few cases where the coercion of the state is necessary and justified, not to guarantee equality of outcome, but to guarantee equality of opportunity for these kids.
However, the mother should not get a single cent for her irresponsible actions.