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I think this horse has probably been beaten to death, but I'd say double check to make sure that the wages are actually non-taxable rather than not subject to withholding or exempt from FICA taxes. Also might be helpful to ask what kind of form they will provide you to report those wages at the end of the year (if at all), if it's a 1099G, I would be extra careful.
I also work for a goverment agency (not a contractor) in a position where my wages are not subject to withholding or FICA. I am required to pay quarterly estimated taxes as a result and I get a 1099-G every year from my agency.
In my case, I cannot file exempt as I still have other taxable wages. I've tried filing online, but it causes an error when I try to leave the field blank like it's done on my W4. I have several W4's to input, all the ones that have Tax paid are fine. But when it comes to the one where there were no Taxes witheld, it cause problems. Tried doing it myself on paper and lost a good chunk of my hair. lol
Even H&R Block had a tough time figuring it out the first year.