There are a lot of reasons to have an emergency fund--to cover a job layoff, to pay your deductible if you get in a wreck, to replace a broken hot water tank--but what if you aren't laid off from your job, in fact you are expected to come to work, yet you won't get paid until maybe sometime in the future? That's exactly what is happening with federal workers who are enduring the government shutdown.
So basically these people don't have time to work elsewhere to earn money since they are expected to be at their regular job yet they are still expected to pay their bills and buy food and pay the electric bill, all without a paycheck. With a good sized emergency fund this will be survivable. With no emergency fund, this will be a crisis within a week or so.