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.

Well why don't they use the same chemicals to knock you out wot they use for surgery and that?

I'm not reet sure. Perhaps it's something to do with how they'd react with the kill-you chemicals, or perhaps it's expense. Opponents to the injection suggest an alternative, I think, but proponents are following an "if it ain't broke don't fix it" path.

Aye, don't want em having a bad reaction and coming out in a rash or summink (nod)

I dunno, I was thinking they were awake, more so since Rowans posts above

I'm wazzed and in parts exotic, but if either of u've got the inclination, there's a French revolutionary philosopher who did some pretty extreme experiments in which he grabbed guillotine victims from the Tumbrel and then roared questions in their ear. There seems to be some kind of confirmation of continuing conscioussness. Which is nice. sorta.