Does a vendor have rights to not do business with a potential client?

B"H
In the good ole USA a baker has got himself into hot water.

http://www.katu.com/news/business/Did-a-baker-break-the-law-when-denying-service-to-same-sex-couple-189450071.html?tab=video&c=y

Bully gay rights groups are gearing up to have their cake and darn well eat it too. They are taking him to court.
A crazy situation.   Why could he not have looked in his book and said "oh, dear, you said the wedding  is next week. 
I am booked until next June. Sorry.
It's like "Darn. Do I have a right to work at producing something for a buyer of my choosing? 
Yes sir, I do so, SIR.