why can't you make an estimated payment after January 15, 2020???? 

One reason is probably after Jan 15 you will be filing your return with a payment or after Jan 15 you will be paying a payment with an extension.

See page 2 when to file, https://www.irs.gov/pub/irs-pdf/f1040es.pdf

* You don’t have to make the payment due January 15,
2020, if you file your 2019 tax return by January 31, 2020,
and pay the entire balance due with your return.

My point is that If you owe money , you are not ready to file your return and it’s after January 15, 2020 , you can still make a payment ..... you could be subject to interest on a payment that was otherwise due on January 15 , but it will reduce / shut off the interest clock if you pay an estimate after January 15, 2020:

I have never heard of the IRS refusing money!!! 

Yes you can do that but the IRS and state tax collectors like to get their money  by each quarterly due dates and you will probably be fined for late payments for the first three quarters.

https://turbotax.intuit.com/tax-tips/self-employment-taxes/myths-about-quarterly-taxes-for-the-1099-...

If you can prove you earned all the income in the quarter there is a form to use for that. And if you have any income by W2 earnings if you pay a lump sum from that they count that as if paid equally through the year.

All well and good and true HOWEVER go back and read the thread .... @DoninGA ’s response infers you CAN’T make a payment after January 15, 2020 .... my point is you can, but depending on your liabilities there MAY be interest due for late payment - 

The question was concerning a 2019 estimated tax payment.  The answer is correct.  A payment made after 01/15/2020 is not a 2019 estimated tax payment

Call if what you want, It is still a payment that the IRS will accept 

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.

Thank you very much! Also, I live in PA - I can make one estimated payment to them as well? I had to cash out my Mom's 401k in October before the 5 year window after her death closed in November and I want to make sure I pay extra now rather than in April.

Thank you again so much!!!