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The setting you put on your w4 was saying "hey there, my spouse doesn't work, I'm filing married and claiming 2 kid, so don't deduct any federal income tax unless I make over 884.00 a week in taxable income".

Do you have any pre tax deductions that are bringing your taxable income around 884 a week?

My spouse doesn't work, my taxable income every week is ~869.

Then your employer is doing what you asked. You have a very minimal federal tax liability, so you don't need significant withholding.

The only thing withholding would do is pad your federal refund. Instead, just set up an auto deposit into a savings account.

Based on the numbers provided, you'd have about a $716 tax liability. But do you have insurance or retirement contributions taken out of your pay? And how long is a pay period?

Edit: at ~$869 weekly taxable income with those W4 settings you shouldn't have any taxes being withheld and you won't be paying any taxes.

I have both taken out and a pay period is biweekly.

$869 per week is $45,188 per year. minus standard deduction of $27,700 is $17,488 taxable income. Taxes on that income is $1,749. Minus child tax credit of $2000 is you don't owe anything in federal income tax.

But based on federal income tax table they should be withholding about $6,000 in federal tax.

No, where did you get that impression from? Are you looking at publication 15t?

Your Federal taxable wages would need to be around $98,000 after pre-tax deductions to have $6000 in tax liability with 1 kid. Not sure how you got the numbers you did.

With the marginal tax rate chart.

No I was going off the marginal tax rate.

That would be incorrect then. What they are withholding is correct.

I suspect the chart you're looking at is based on taxable income, so you'd need to deduct off your standard deduction before using the table. Also, it's not taking into account the child, which wipes away your tax liability.

You need to factor in the standard deduction of $27700, the fact that tax rates are progressive so the remainder of your taxable income is all in the 10% bracket and the CTC reduces your final taxes by $2000.

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It's not payrolls job to determine what your personal tax liability is. It's their job to withhold based on how you fill out your W4. I would suggest plugging all your household's info into https://www.irs.gov/individuals/tax-withholding-estimator and based on those results it will tell you how to fill out your W4 which you then give to your company.

No. Move the child tax credit to the end. After finding your tax, then deduct 2000 from the final tax calculation.