Most likely.
However, to remove the expense of continually having to defend this kind of thing in court, states should implement a nitrogen chamber. Stuff the condemned in the chamber, fill it with nitrogen, wait half an hour, then cart them out. It's simple, cheaper than dirt, completely painless, and quite effective.
My personal lack of confidence in the American legal system causes me to not support the death penalty as fully as I once did, but if you're going to do it, this is the best way. The condemned won't even know he's dead. He drifts off to sleep rather quickly, and wakes up with a demon standing on his chest. If, through some serious miscarriage of justice, an innocent man was convicted, he isn't forced to suffer needlessly, and will get his just reward in the afterlife.
The state shouldn't be at the mercy of drug companies or whackjobs in these instances.
I’m in favor of the firing squad. Cheap, guaranteed, and volunteers would be easy to find.