Is it normal not to be able to lift your head off the floor when lying down flat after having Botox in the neck bands?

The muscle that lifts the head, called the platysma, is the same muscle that causes neck bands. Injecting the bands will weaken the platysma. In some patients, there is a fine line between achieving a nice cosmetic result by eliminating the bands and not weakening the neck muscle so that it is hard to lift the head.
The platysma's weakness will resolve as the Botox wears off. Ask your doctor to inject fewer units of Botox in this area next time. 

Thank you for your question. What you are experiencing is not unusual and as long as you are not having difficulty swallowing there is no significant problem. However, this should get better over the next couple of weeks. Please make you injector aware of this. Best of Luck!

While some weakening of neck muscles maybe possible after Botox injection for neck bands, it's not something commonly seen with conservative does. I usually inject 8-12 units per neck band and don't inject more than 50 units into the neck. This avoids most issues. That being said, as long as you are not having any difficulty swallowing, there is nothing to worry about. The Botox will wear off over the next 3-4 months.