If you want to make a fuss, the IRS will most likely come down on your side.
If you want to go along to get along, you should expect to be paid 7 to 8% more to compensate you for the additional tax you will pay. You will effectively now be paying the employer share of FICA (social security and medicare tax), in addition the the employee share.
The IRS considers anything in
box 7
of 1099-MISC to be self employment income. Enter the 1099-Misc income, at Other
Common income / income from a 1099-MISC . TurboTax (TT) will complete Schedule
C or C-EZ for you and allow you to deduct any expenses associated with this
income. You'll also have to pay self employment tax (social security &
Medicare) on any profits greater than $400. These types of payments are
frequently done this way. Your "employer" is not the only one.