Depends on your income, and how you filled out your W-4. Assuming you claimed single with no dependents, you should have federal tax taken out if your taxable income is more than $288 per week or $1250 per month. Remember that health insurance premiums and most retirement contributions are pre-tax, so if your gross salary is $2000 per month but you contribute $500 per month to the retirement system and $250 per month in health insurance insurance premiums, your taxable income will only be $1250 per month.
If you claimed additional dependents or are married, the tax threshold is higher.
To calculate your correct withholding, use this IRS calculator. Make sure to answer all the questions, including questions about a spouse's income (if you have a working spouse) and any dependents. If you are married, you and your spouse should run the calculation together, and both file new W-4s at the same time based on the recommendations.
https://www.irs.gov/individuals/tax-withholding-estimator
