I think we all tend to have poorly calibrated mental models of this because coverage of war tends to focus on the heaviest action and worst of the devastation.
I don't mean to downplay how awful that can be, or how far the effects can reverberate (even generations later), but like... the vast majority of people still go about their daily lives, doing their usual jobs, doing the mundane things, even having fun, supply chains and infrastructure and institutions seem to be quite resilient, etc. Locally and individually, everything can change in an instant in combat (even then, most people walk away from that and continue their lives), but nationally things can keep rolling along as war drags on much more slowly than we all might expect or hope.
So I have little doubt that the IRS would keep doing its thing, and tax returns would need to be filed (albeit maybe with extended deadlines), even in the wake of a nuclear attack. I suppose the question is how much do things unravel in a scenario of nuclear counter-attack, and counter-counter-attack, etc. for which we have no historical precedent to think about.