Yes, there are minimum income limits that must be met before federal taxes are withheld.
Those limits depend on your filing status (Married Filing Jointly, Head of Household, or Single or Married Filing Separately), the number of withholding exemptions you are claiming on your Form W-4 and the frequency with which your are paid (weekly, bi-weekly, or monthly).
For example, a person filing as Single, claiming no withholding allowances and paid weekly would not have any income tax withheld until their weekly earnings exceeded $80. (This would likely explain why employees with only 4 hours in a pay period would not have any income tax withheld).
A person filing as Married, with the same number of withholding allowances and paid weekly, would not have any income tax withheld until their weekly earnings exceeded $235.
The method for calculating withholding depends on how the payrolls are prepared (automated or manual) and when the Form W-4 was filled out.
For a complete explanation of how withholding is calculated, please go to Publication 15-T (2021), Federal Income Tax Withholding Methods.
