Andrew Dugan has this report for the Gallup Poll with the above title.

Still, there is no denying that the opponents have made inroads.  The number of people answering "not in favor" to Gallup's poorly worded basic question is the highest it has been since before Furman v. Georgia in 1972, when the Supreme Court's audacious act of judicial activism precipitated a sharp drop in opposition and a sharp jump in support.

On the better-worded, but still less than ideal, question of whether the death penalty is presently imposed too often, about right, or not often enough, the sum of about right and not enough is still 2/3 of the population.  That remains a powerful supermajority in favor.  Dugan writes:

By many metrics -- the number of states that have banned the death penalty, the number of executions carried out or the actual population of inmates currently on death row -- the death penalty appears to be losing popularity in statehouses and courthouses across the country. But the public at large continues to support the use of the death penalty. A majority continue to assess the punishment as applied fairly, and a plurality wish it were applied more often.

The biggest problem is that the other side has all the megaphones.  Academia enforces adherence to anti-death-penalty dogma.  We saw that when the economists who dared to publish studies showing deterrence were hounded out of the field.  In journalism, balanced reporting is the exception, and propaganda pieces on the anti side dominate.

Yet despite all that, the side of justice still has two-thirds.  It's both discouraging and heartening at the side time.