I predict that either that happens, and in that case please lay off the entire IRS, then simply don't give people tax returns while demanding they keep paying with automated systems that don't get told people already paid. Or the month after the shutdown passes there's a hiring craze as government agencies desperately try to fill positions left vacant, causing just as much if not even more trouble due to the loss of so much institutional knowledge and a workforce unready for the task ahead.
Either way, trouble.
Either way, trouble.