It depends on how your projects/team is funded. I’ve been on teams where a shutdown had a pretty immediate impact (people had to be shuffled around to other projects in the short term). I’ve also been on teams that get all their funding at the start of fiscal, so a shutdown doesn’t impact them until they need to be funded again.

These days it seems like management tries to keep a buffer so they can operate for a little while during a government shutdown. That being said, there are a variety of funding sources and it wouldn't be fair for some teams to be allowed to keep working while others could not, so they'll typically shut basically the whole lab down once they run out of extraordinary budget measures.

Also, if there is an actual shutdown Congress usually retroactively pays the federal employees who were furloughed but it doesn't typically apply to contractors. (DOE labs are staffed by contractors rather than government employees so that they can pay more than the government pay scales)