A 1998 poll in New York found that if given a choice between life without parole and execution, the majority of people would favour the former. So public support for the death penalty is not as deeply entrenched as commonly supposed. Indeed, support for capital punishment in Texas is at its lowest level since the 1960s (it's now 68%, down from 86% just five years ago).
If the facts about the death penalty were more widely known, it is unlikely it would be so well supported. In fact, what is wrong with 20 or 25-year (very long!) sentences for murder, when you take into account that the rate of recidivism among murderers is less than 1%? Only 0.3% of convicted first-degree murderers in the US go on to murder again. In many countries, the recidivism rate for murder is smaller than that. The rate of people convicted for petty offences who go on to murder, on the other hand, is higher than the recidivism rate for murderers.
The point of a representative democracy - the form of government of the United States - is that legislators are those able to find out about a topic and come to thoughtful conclusions on it. These conclusions need not be the same as those that a majority of uninformed people have reached. (In Britain a couple of years ago, an experiment was done where people were given both sides of the story on monetary union before being asked to give their opinion. The debate caused them to shift considerably to the pro-monetary-union side. This exercise is called deliberative polling.)
The death penalty is cruel, inhumane, breaches international standards of human rights, is applied disproportionately to ethnic minorities, is used against the mentally ill and retarded, has been abandoned by the majority of countries of the world, and always risks killing the innocent.
Kill the death penalty.