My husband travels extensively for work, different locations every week. The payroll company has stopped deducting local taxes from his checks. They state that he is not required to pay out of state tax when he travels and since he is not technically "in town" the local taxes are no longer deducted from his check. The city we live in however, would like their full cut from his yearly wages. Shouldn't the city taxes be deducted regardless of where he happens to be traveling on any given week?

Shouldn't the city taxes be deducted regardless of where he happens to be traveling on any given week?

Yes, they should, assuming his trips are considered temporary (I, e, he is not actually being transferred to a new location). But even if the company does consider him to be physically transferred then they must withhold the appropriate local taxes for his new location. I am assuming here that your husband is a W2 employee, and not a contractor.

I suggest that your husband request that the company restart withholding for local taxes where he lives. If they don't then your husband will have to file quarterly estimated tax payments on his own or risk facing interest charges for late tax payments when he does his yearly tax return.