Sorry to perpetuate this off-topic discussion, but one can certainly make a Q4 estimated tax payment late, after January 15. It might or might not be able to be done through IRS DirectPay after January 15, but it can certainly be done by mailing a check with the Q4 Form 1040-ES for the year to which the tax payment is to apply. Doing so will reduce or stop any further increase in the interest penalty for the amount that was required to have been paid by January 15 but wasn't. I did this myself with regard to my 2013 taxes when I didn't remember to make my Q4 estimated tax payment until late February.
An alternative to making a Q4 estimated tax payment is by January 31 to file an pay the full balance due and the payment for the Q4 tax liability will be considered to be timely.
