During one past Government shutdown the National Park Service followed the instructions of their politically appointed leaders and closed all facilities to the public. One such location closed to public access was the Washington Monument. Tax payers who had traveled to Washington, D.C. and local business owners immediately started complaining to their Congressional Representatives and the Park Service was ordered to immediately open the gates of the internationally recognized Monument. It was public inconvenience and outrage that got this one specific location exempt from the closure order.
A Park Superintendent who I later worked for was reluctant to ever close any area or facility due to what he referred to as the "Washington Monument Syndrome."
What many people do not realize is the dependence of communities across the country on the dollars pumped into their economies by tourism to National Parks. As an example academic studies have shown that approximately $2.3 billion are pumped annually into the communities on or near the Blue Ridge Parkway through Virginia and North Carolina. A cancellation of travel plans by visitors for any period of time will have a direct impact on hotels, stores, restaurants, private campgrounds, and their employees.
Should the Government Shutdown occur it may be interesting to see how long it takes for the "Washington Monument Syndrome" to take affect in individual Congressional Districts.
Here is a related article that outlines the possible impacts of a closure on businesses in the area of Yellowstone National Park: