... Conservatives don't want any safety net to help support the mother and child or pay for medical costs.
Wrong Consevatives support a "safety net". Conservatives don't support generation after generation of a welfare state hammick. The problem is liberals want to take social welfare spending to an extreme.
Baloney! If the Conservatives had their way they would dismantle Social Security (a ponzi scheme), Medicaid (a failure) and Medicare and the food stamp program. You would probably get rid of unemployment insurance too since the employer has to contribute and that is money out of his pocket. There are dozens of other lesser safety nets that you would dismantle also.