Is there any reason why taxes wouldn't be taken out of paycheck?

Your first step would be to check with your employer's HR or payroll office.  It might just be a mistake.

Maybe your pay is low enough not to have any taxes withheld as married.  If you want to have tax withholding you can change it back to Single.  What you claim at work doesn't  have to match your actual tax return.  I'm married but claimed Single at work to have more taxes taken out.  

@8894db4ac916 the W-4 mimics the tax return.

So by switching from Single to Married, the W-4 follows the standard deduction  and tax tables for a Married Couple.  Therefore, the withholdings are less.

It is quite possible that if your income would produce a refund (including the impact of the child tax credit and EITC you may be eligible for), nothing is withheld because you are still due a refund in April.  

In that circumstance, withholdings are returned to you in April all you did was create an interest free loan to the IRS. 

It is highly unlikely that Payroll is incorrect; it is more likely that your income is low enough that no withholdings are required and you still will receive a refund in April.