Moody’s warns federal shutdown would be ‘negative’ for US debt rating

Because federal “shutdowns” are partial spending shutdowns from lack of spending authority, they don’t change the substantive rules on taxation, and they don’t stop enforcement action for violaltions of tax laws that occur during the shutdown.

If the shutdown lasts long enough, they'd probably stop. But once it has reached that point, the dollars you're paying wouldn't much matter anyway.

Exactly how long depends on just how much stuff gets shut down. This time they're looking at shutting down everything; no appropriations bills have passed. If it reaches anywhere near 35 days, the length of the last (partial) shutdown, your taxes would be moot.