As on most issues, I would say the solution is simply to allow individual choice to operate. Let the technology of life extension develop (no one can stop this anyway), and then let every individual decide how much, if at all, to avail himself of it. Those who believe that submission to the process of aging and natural death is somehow morally obligatory should be free to follow that route. The rest of us will make our own decisions based on our own values.
It does seem, though, that conservatives ought to welcome this, considering how much they lament the falling birth rates throughout the developed world. The gradual disappearance of aging and death would render this problem irrelevant. Of course, as the death rate fell to zero, we would eventually reach the point where even a very low birth rate meant steady population growth, but that's something that conservatives generally believe we can handle (and I agree).
To paraphrase advocate Aubrey de Grey: Would widespread use of life-extension technology lead to problems? Obviously it would. Would it lead to any problems as serious as continuing to have a hundred thousand people die every day (the status quo)? No.