Never claim exempt on your W-4.
If the job is low pay, you will automatically have little or no tax withheld, if the job is middle income or higher income, you will have approximately the correct tax withheld for your situation. In other words, your withholding is supposed to be self-adjusting.
The whole point of the W-4 is to make sure you pay enough into the system but not too much. It doesn't actually change your tax liability, which is only calculated on your tax return. If you are not legally exempt from tax (almost no one is) but you claim exempt on the W-4, you may owe a large tax bill at the end of the year plus interest and penalties.
