I am losing my job in March, they are giving us a severance package and a bonus for staying, can I go tax exempt for a few months or would it be better not to?

[VolvoGirl]

No.  Exempt is never good.  You will owe tax on all your income including severance and bonus.  And if you get another job you owe tax on your total income for the year.  You should have withholding taken out.

[rjs]

You do not meet the requirements to claim exemption from withholding. In order to claim Exempt in 2020 you must have "had no federal income tax liability in 2019 and you expect to have no federal income tax liability in 2020." But you were working in 2019, so you had tax liability, and you will have taxable income in 2020. So you cannot legally claim Exempt on your W-4.

"Tax liability" means the total tax for the year on your tax return. It does not mean an amount due that you have to pay when you file your tax return.