For those who Civics is rusty. It is the federal government that is shut down. That may mean no access to National Parks, National Forests, BLM land or similar FEDERAL properties. DNR (Department of Natural Resources) is a state agency, like Fish and Wildlife and like State Parks. They are still in business. Your Discovery Pass money went to support 1) state parks, 2) WaDFW, and 3) DNR. They are still open. As Merrill appears to be DNR, its gate should still be open, business as usual for state agencies.
If you have been using your Discovery Pass or the parking pass that comes with your fishing license to access federal land, such as Leech Lake or Coldwater Lake and you haven't gotten a ticket for not paying the right agency, you've just been lucky. Federal lands requires you to pay access fees to the feds. The state and feds do not share revenue.