No, that would only set the minimum wage, and even that would only apply to businesses that have interstate facilities.
Coverage is broader than this.
Government defines "interstate commerce" very very broadly.
http://www.dol.gov/whd/regs/compliance/whdfs14.htm
".....employees are protected by the FLSA if their work regularly involves them in commerce between States ("interstate commerce"). The FLSA covers individual workers who are "engaged in commerce or in the production of goods for commerce."
Examples of employees who are involved in interstate commerce include those who: produce goods (such as a worker assembling components in a factory or a secretary typing letters in an office) that will be sent out of state, regularly make telephone calls to persons located in other States, handle records of interstate transactions, travel to other States on their jobs, and do janitorial work in buildings where goods are produced for shipment outside the State.
Also, domestic service workers (such as housekeepers, full-time babysitters, and cooks) are normally covered by the law."
Why would a cook be covered?
They'd argue the Interstate Commerce Clause applies because food was grown in another state, energy used was produced in another state, or the cook's clothing was produced outside of the state. There is nothing the fed gov cannot regulate, except perhaps buying a melon at an Amish roadside stand.
