Executive branch of government oversees the function of various departments of national government to ensure that the government is functioning and that the necessary social services are delivered to the people and is therefore should be the responsibility of the national government. The legislative department which is composed both by the lower and upper House of Congress pass laws and other measures which has national (and state) implication such as passing of national budget or the Obama Care healthcare program. Given the implication of its function to the national government, the legislative department should be the primary responsibility of the national government.
The two areas that should be the primary responsibility of the state governments are the judicial and legislative function. Judicial branch of government are composed of our courts and their corresponding functions of interpreting the law and dispensing justice. Given that laws in each state vary to some degree (i.e. gay marriage, legalization of marijuana, imposition of death penalty), it should therefore be the main responsibility of the state government. There is also an aspect of the legislative branch of government which is the domain of the state government such as the crafting of laws of state councils that only pertains to their state making it a responsibility of the state as well as national