Car dealership asking for more money for an add on.

Location: Illinois, US

I recently bought an suv and as part of the purchase I paid for a tow hitch to be added. Now after I brought it in for the service, they are claiming they misquoted the price ($1,575) and that it will actually be about $3,000. Am I wrong to play hardball and say they are contractually obligated to add the tow hitch? They are currently trying to make me pay all, or some of the difference in price.