It's a divided issue.
Opponents of lethal injection reckon that the chemical used to knock you out is actually only very short acting (which is why you're not allowed to use it for surgery, or for putting animals down), whilst the paralytic effects of the other drugs are not. So, basically, you get knocked out for a minute or two, wake up in paralysis and have to endure 30 mins of excruciating pain as you die.
Proponents disagree.