If it happens, and it might.....I think no federal legislator should get their tax-payer salary, and their health benefits should immediately be frozen.
Their salary comes from a "different revenue stream" than soldiers and their families, or other "non-essential" federal workers, but tough shit. If they can't do their damn job, and we can't really fire them with two weeks notice, we can at least withhold their pay. Just like what would happen to other "civil servants".