The federal government shutdown starts today, and you shouldn't worry. Here's some history on shutdowns: A Brief History Of Federal Government Shutdowns
The short version is that there have been 17 government shutdowns in the past, the longest lasting 21 days. Only "nonessential" federal workers are affected, bringing up the question "How is this a shutdown and why would nonessential personnel come back to work anyway?"
The only thing most usual people will notice is that you can't go to a national park. Great, turn those over to state governments leave the federal government "shut down" and we'll be far closer to the structure outlined by the Constitution.
That won't happen. Congress is likely to resolve this fast, and if past shutdowns are any guide, will get back pay for the furlough time, so they're getting a paid vacation at your expense.