They will be declared essential workers. And they will work, or forever give up any hope of a Federal job and pension.
I really question the accuracy of the article you provided, as of the date published ALL Fed workers had gone “nearly two weeks” since being last paid.
They’re paid every 15 days.
And you can have that warm, fuzzy, safe feeling thinking about the possibility that your air traffic controller is more worried his house under foreclosure and being late to work because his truck was repossessed than his job.