And there are some contracts and missions in which the money has already been paid, so they will continue, so long as there is a government rep around to oversee the task.
Post Offices aren't funded directly by the Government, they maintain operations, though they might cut hours and services for the duration.
National Parks will shut down. Which will affect the local economy around those parks.

One of the worst thing about a government shutdown is that people can't use their leave to keep being paid during the furlough, if they have it. They have to go home to figure out how to make up the lost wages.

Haele

are a national security issue and are protected. Even Posse Comitatus doesn't apply.

Sara Sanders said at today's W.H. press briefing that Trump will be flying to Mar-a-Lago this weekend.