I noticed that there are no federal taxes coming out of my check. Will I owe the IRS money?

[Bsch4477]

See this. 
https://www.irs.gov/individuals/tax-withholding-estimator

[xmasbaby0]

You have not said whether you are a W-2 employee or if you are an independent contractor.   If you are a W-2 employee----is Social Security and Medicare being deducted?    If not, you need to determine if you are going to be treated as an independent contractor and get a 1099NEC.   If that is the case, then you will owe self-employment tax for Social Security and Medicare as well as ordinary income tax.

If you are a W-2 employee and the employer is simply not taking out federal or state income tax, but is withholding SS and Medicare, you can use the W-4 calculator to see if you should be having more federal tax withheld.

https://turbotax.intuit.com/tax-tools/calculators/w4/ 

https://www.irs.gov/individuals/tax-withholding-estimator

https://www.irs.gov/pub/irs-pdf/fw4.pdf