I should imagine it would be like having your blood taken
Not really. Lethal injections in the US usually involve administering three drugs. The first is a sedative, the second causes muscle paralysis and respiratory failure, the third induces a heart attack.
People who have survived lethal injections paint a pretty horrific image of the second two drugs. They described being unable to move, speak or breathe as fire flows through their veins.
The fact that people have survived lethal injections should itself demonstrate the problem with it. Executions are frequently carried out without a trained anaesthesiologist at hand. This makes it more difficult to determine whether the drugs have been administered properly and whether the prisoner is fully unconscious before the second and third drugs are administered. There have even been accounts of prison staff struggling to find a vein at all and resorting to repeatedly jabbing needles until they think they've found one.
If every step of a lethal injection goes smoothly then yes, it's a reasonably painless death. If even one step goes wrong, it's an excruciating death. The simple fact of the matter is that we just don't know how many prisoners have died in agony while being unable to tell prison staff that something has gone wrong.
Perhaps some people are comfortable with prisoners suffering a painful death. I have to admit that I wouldn't lose too much sleep if it had happened to Hitler. However, I recognise that this is due to my own hatred of them and my desire for revenge. I can't claim it's based on any noble desire to see justice done.
As a final note, I'll add another reason why I oppose both the death penalty and miserable prison conditions. Some prisoners are genuinely innocent. We can only provide estimates of how many death row inmates are innocent but the most common figure I've seen is around 4% That's disturbingly high.
Even though some people are so monstrous that I genuinely don't care if they suffer or die, I have to keep in mind that my vengeful streak can easily end up being directed towards somebody who did nothing wrong.