After the tax day, I realized I have withheld too little tax so far this year. So I need to catch up.
But even if I put the extra withhold to be the same as my take home pay, the tax at year end is still not enough.
What will happen if I put more extra withhold on my W-4 so that my take home pay would be negative?
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I doubt the payroll will allow that to happen.
You can make quarterly estimated payments to catch up.
I think it’s too late to make estimated payment.
When I change my W-4, the system would approve everything I entered automatically. I just don’t know what will happen next 
If you think that, how can changing your withholding help? I normally under-withhold for the first 6 - 8 months of the year. This usually results in my tax return payment being just under the amount which triggers a penalty.
It’s too late for Q2, but there’s still Q3 (9/15/20) and Q4 (1/15/21).
Did you have a huge bonus payment or something in the first six months? Otherwise I don’t see how you could owe more than your take-home.
I would be surprised if you got a negative check (a bill?). That would be hilarious.
Yes I sold some long held stocks.
Wait I thought the estimate payments have to be evenly distributed to avoid penalty? I have never made one before.
This is just one reference point so it might not apply to you… In my case, years ago I had some 1099 contract-type monies coming in for a few months. In December I sent the IRS a large payment thus avoiding the penalty.
I think this might be true if you were self-employed and elected the Accrual Accounting method for recognizing the business income. There’s no requirement to evenly distribute payments if you use the Cash Basis Accounting method, which IMO is easier and more applicable for individual taxpayers and likely many small businesses that do not have generate stable or guaranteed income. In other words you pay the tax in the same quarter you received/recognized/realized the income.
More info here if you’re interested: https://www.irs.gov/taxtopics/tc306
"Penalty for Underpayment of Estimated Tax
If you didn’t pay enough tax throughout the year, either through withholding or by making estimated tax payments, you may have to pay a penalty for underpayment of estimated tax. Generally, most taxpayers will avoid this penalty if they owe less than $1,000 in tax after subtracting their withholdings and credits, or if they paid at least 90% of the tax for the current year, or 100% of the tax shown on the return for the prior year, whichever is smaller."
Can you reach the safe harbor by just withholding less than your take home pay? It’s likely going to be much easier to do that. If your pay is regular, subtract about $10 or so ,(preferably more) from your ,“take home” amount and add that flat amount of extra withholding.
To answer your question, they’ll withhold as much as your check will accommodate. If you request $1,000/week extra withholding and your check is for $400, they’ll withhold $400 that week.
But as others have said, you can make irregular estimated payments. As long as you arent intentionally waiting until January 2021 to pay your entire 2020 tax bill, you’ll be fine. Estimated payments serve two purposes - to pay the tax on regular income, and to account for one-time income. If you have a large one-time gain, you can (and are supposed to) make a large one-time estimated payment as well.