When people are hearing/seeing a performer for the first time, they are making their own judgment as to whether or not the performer is worthy of a listen. If the performer plays an original song first, the listener must then judge the quality of the song as well as the quality of the performance. Although this doesn't sound like a huge undertaking, it actually can be.
The average American is in 'sensory overload.' They are bombarded by media messages at every turn. They are forced to make split-second decisions on where to direct their attention.
If you lead with a popular cover song, the listener is drawn by the familiarity of the tune and will be more likely to pay attention long enough to pass judgment on your performance. Once they like you, they are more likely to listen to your original music and obscure covers.
Think of it in terms of the direct mail business. Getting people to open the 'junk mail' is the hardest part. Once they pop the envelope, the chance for a sale goes up exponentially.
Open with a cover and you'll find that you'll have more people paying attention to your performance.