Does federal government issue drivers licenses?
Only to members of the US military to drive military vehicles. States issue regular driver's licenses.
Amongst other things, the State Governments are responsible for the provision of Law enforcement, public schools, hospitals (though this is progressively becoming a federal issue), issue drivers licenses just to name a few. In the Australian system, the states have the right to legislate on any issue where the commonwealth hasn't, or doesn't have the power to legislate, excepting a few things like the states can create their own currency, raise a army etc.
The Constitution states that any powers that are not reserved to the federal government belong to the states and to the people, but it does not specify what those powers are. That is one reason why the SCOUS settles constitutional cases. It also why states issue driver's licenses, and the Federal Gov't does not.
Not legally, no. New York and Pennsylvania will only issue drivers licenses or non-drivers licenses to legal residents of their respective states. If you move out of PA, for example, you are no longer eligible for a PA drivers license. If you use a license showing that you live in PA when you actually live in NY, then that is fraud.
Why do many people feel that Federalism can be defined by examining a dollar bill and a drivers license?
Maybe federalism means the relation between the national government and the states, something that was spelled out in the Constitution in 1789. Notice that a dollar bill (representing the money circulating in the U.S.) is an example of the federal government at work, since only the federal government can issue money. Driver's licenses are issued by each state, one of the responsibilities that was left to the individual states because it was not specifically enumerated…