Sorta, except that we now don't consider ourselves to be seperate countries, except for Texas, which was before 1845 and joined the US by treaty. Just consider the name of the country, United States of America and how the nation was formed. Each of the 13 original states more less considered themselves to be seperate nations with a common need. We fought a war over this issue (among others) in 1861.
Each state
theorectically governs its area with the feds handling the international aspects of national government. Local law enforcement, schooling (K-12 and colleges), criminal and civil courts are the responsibibilty of the states. Issued that affect multiple states are governed by the Feds, such as interstate commerce, national defense and disputes between states. The nature of our national govenment has changed significantly, especially since 1913, when the US Senators no longer were chosen by the state legislatures. Before that, the Senators were to look after the needs of the
govenments of the states they represented, with House of Reprehensibles representing the needs of the
people themselves of the state. As a result of the
17th Amendment, they no longer were beholding to the needs of the state govenments and the power and spending habits of the federal government has up unbelievably since then as
Federalism * has been damaged greatly.
*This article will explain our method of government better than I have here, if you are in the mood to read.