There is no difference in a severance payment and any other payment from an employer to an employee as far as what must be withheld. It will be subject to Social Security and Medicare tax withholding of 6.2% and 1.45%, respectively. It will also be subject to federal and state tax withholding. That can vary. They can withhold according to your current Form W-4 and state form, or they may withhold a flat 22% as if it was a bonus payment. You should be able to specify the amount you want them to withhold for income tax. That is all that is required to be withheld. There could be additional benefit withholding if you are remaining on the employer health insurance plan, or if you want a 401(k) contribution withheld. All of those things should be negotiable.
The above assumes your employer will treat you as an employee (report the income on your W-2) and not as an independent contractor (report it on a 1099-NEC).
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