On polling and death

  "If a hopelessly ill patient, experiencing unrelievable suffering, with absolutely no chance of recovering, asks for a lethal dose, so as not to wake again, should a doctor be allowed to give a lethal dose or not ?" 
"If someone with a terminal illness who is experiencing unrelievable suffering asks to die, should a doctor be allowed to assist them to die?"
I wish I had a dollar for every time I've heard someone say that euthanasia & assisted suicide legislation has popular support and that 'the will of the people' should be endorsed by our parliaments.
The above questions are two iterations of polling questions in Australia over recent years. Both returned a 'yes' answer in upward of 75% of those polled.
Polling on euthanasia is always fraught with difficulty. How do you accurately describe a situation of a person's death when every situation is inherently different? What do terms like hopelessly ill, unrelievable suffering, a lethal dose and assistance to die really mean?
Online newspaper polls have an additional level of concern. As Dignity with Dying Tasmania points out: Voters are not a random cross section of the Australian community but a group of self selected individuals who may live anywhere in the world and whose only qualification is that they are able to access the internet. Precisely so.
But the question about polling holds a certain interest for the body politic in as much as politicians, by their very nature, are always interested in polls as they seek to divine a sense of any mood in the electorate that may have an effect in the ultimate poll - the ballot box.
Polling does have an influence, certainly; but should it be the ultimate device for a politician to make his or her decision on an issue of such moment as euthanasia & assisted suicide?
If polling were the determining factor in legislation, Australia would still endorse (or be prepared to re-endorse) capital punishment for serious crime. Polls on this issue are somewhat volatile and come under the influence of contemporaneous criminal acts, such as the Port Arthur massacre in Tasmania. But here, even recently in an online article suggesting that the issue should be revisited, an associated online poll returned nearly 69% in favour.
I'm not suggesting for one moment that capital punishment should be re-instated - I'm against it. But it surely tells us that public opinion, however defined, is at the very least a poor determinate for legislative action.
There's also an interesting contrast here between capital punishment and euthanasia & assisted suicide in relation to risk of abuse. Western Australian MLC, Nick Goiran spoke at length about this at a conference I attended in Vancouver last year. Paraphrasing, he pointed out that the rejection of capital punishment in Australia was in a large degree due to the risk that we might 'hang the wrong person'.
Even after the exhaustion of the police inquiry, the arraignment before a magistrate, the trial before a jury and the possibility of appeals, we still thought that the risk, however slight, of making the wrong decision was too great in light of the fact that the punishment of death was irreversible.
Yet, without the benefit of anything like such an exhaustive process, in euthanasia & assisted suicide some seem to be willing to take a similar risk with human lives.