I made a mistake and underpaid one time about 10 years ago, and the IRS set up a payment plan for me, it was really easy and they were very nice about it, set it at a payment rate I could easily afford, no pressure.
If you don't have payment plan option, this appears to be one of the exceptions that proves the rule against 401k loans. Better to borrow and pay back than to forego the opportunity. EDIT: Assuming that your job is secure and it is highly unlikely you'd be leaving it while the loan is outstanding.