Can you get married while in the US on a visa waiver?

Save yourself a very big headache. DO NOT get married on a visa waiver. It is considered Immigration fraud because you will have immigrant intent. You may not be able to get a greencard, especially if the INS decides that you knew you were going to get married when you got on the plane.

Have your fiancee file for the K-1 fiancee visa. It will take a few months, but what are a few months when you're going to be together 'till death? The K-1 would give you 90 days to get married after your entry to the US.