It is often said that democratic governments rule by the consent of the governed. But this is wrong in two ways. First, many individuals do not consent to what the government is doing. Secondly, when it comes to basic things such as punishing murderers, there is no need for consent on the part of the offender. On this second point, in section 9 of his 2d Treatise on Government: “On Civil Government,” John Locke writes:

I doubt not but this will seem a very strange doctrine to some men: but before they condemn it, I desire them to resolve me, by what right any prince or state can put to death, or punish an alien, for any crime he commits in their country. It is certain their laws, by virtue of any sanction they receive from the promulgated will of the legislative, reach not a stranger: they speak not to him, nor, if they did, is he bound to hearken to them. The legislative authority, by which they are in force over the subjects of that commonwealth, hath no power over him. Those who have the supreme power of making laws in England, France or Holland, are to an Indian, but like the rest of the world, men without authority: and therefore, if by the law of nature every man hath not a power to punish offences against it, as he soberly judges the case to require, I see not how the magistrates of any community can punish an alien of another country; since, in reference to him, they can have no more power than what every man naturally may have over another.

In the prosecution of moral laws so basic (such as the prohibition of murder) that they can be legitimately enforced on those who have not consented to be subject to those laws, it may be reasonable to use a majority vote to determine the particulars of how that law will be enforced. But if a government has no legitimate right to enforce a law in the first place, no vote short of unanimity can make it legitimate to enforce that law. 

Libertarianism and the quite prevalent statism in the world both take relatively extreme positions on what a government can legitimately do. It is logically possible to take an intermediate position: that there are many actions a government has no right to take no matter what supermajority (short of unanimity) is in favor—in particular, for the US, things the government has no right to do even if a constitutional amendment says it can—but that the set of actions permitted to a democratic government are broader than those sanctioned by Libertarian ideas. To me, the principle that there are at least some things no government has the right to do no matter what supermajority (short of unanimity) says it does is the most important principle. The boundary between legitimate and illegitimate actions of government can then be a matter of debate. But it is horrifying to say that a government can legitimately do anything that a large supermajority (short of unanimity) votes for. As Edmund Burke said:

All human laws are, properly speaking, only declaratory; they have no power over the substance of original justice.