Anti-death penalty advocates are gearing up for what they hope will be their most significant victory for a generation, as California enters the final week of campaigning over a ballot initiative that would abolish capital punishment in the state and close the largest death row in the country.

The Californian referendum on ending the death sentence is being closely watched across the US as potentially the most important turning point since the US supreme court temporarily banned executions in 1972. A "yes" vote for Proposition 34 on 6 November would provide a huge boost to abolitionists and send shock waves through the other 32 states that still hand out the ultimate punishment.

California has by far the highest number of prisoners awaiting execution. It has 724 death row inmates, almost twice as many as the next largest, Texas, with 407.

The latest USC Dornsife/ Los Angeles Times poll has supporters of Proposition 34 on 42%, just three points behind those who would keep the death sentence in place. That's within the margin of error, suggesting a statistical tie.

The abolition proposal is being backed by several high-profile individuals and organisations, including the conservative Fox News talk show host Bill O'Reilly and most large California news outlets. One of the proponents of the initiative is Jeanne Woodford, former warden of San Quentin prison outside San Francisco which houses California's death row.

Woodford told the Guardian that having spent more than 30 years in the state's criminal justice system, she had come to the conclusion that the death penalty was indefensible. "It is broken and ineffective. It doesn't provide greater public safety or enhance our social morality in any way."

During her time as warden of San Quentin, she presided over four executions including that of Robert Lee Massie who was put to death in 2001 for two separate murders having "volunteered" to die by refusing to pursue any appeals.

"In reality, Massie's execution went ahead because he didn't want to live," Woodford said. "So we were helping him with his suicide – that's a lot to ask of any public servant, and in any other situation it wouldn't be considered appropriate."

Woodford added that it was only after she stood down as warden that the full impact of having effectively acted as executioner on four occasions hit her. "I didn't let it destroy me as I became determined to do something about ending this policy – if I wasn't working towards something positive it could have eaten away at me."

Ahead of the vote, the abolition campaign, Yes on 34, has been intensively running TV and radio adverts across California. The TV advert is narrated by Hollywood actor Martin Sheen and features the story of Franky Carrillo, who spent two decades on death row for a murder he did not commit.

The campaign's organisers have been deploying several arguments in the hope of attracting voters to the abolitionist cause. In addition to the moral argument that capital punishment can lead to innocent people such as Carrillo being put on death row, they are pushing a more pragmatic financial line that might appeal in these economically challenging times.

A recent study carried out by a senior judge found that the death sentence costs California an extra $184m a year above and beyond what it would be spending were death row closed and all its inmates transferred to life without parole – the alternative put forward by Proposition 34. The overall cost of death row to the Californian taxpayer, including the inflated expense of capital trials, heightened security in prison and endless legal challenges and appeals, was put at $4bn since 1978.

The savings that could be made by switching to life imprisonment would allow an additional $100m a year to be spent on investigating serious crimes in a state in which a shocking 46% of murders and 56% of rapes go unsolved. Increasing the clear-up rate of those crimes would be a far more effective deterrent, supporters of the proposition argue, than holding people on death row for many years with very little to show for it – there have been just 13 executions in California since 1967 and the practice has been legally on hold since 2006.

Support of victims. families

As a symbol of how ineffectual California's death row has become, the most probable way for someone to die on death row is now through old age. Since 1978, 84 inmates have died from natural causes or suicide.

The other powerful channel through which supporters of Prop 34 hope to garner votes is to highlight the stories of families of victims of murders and rapes who want to see the death sentence abolished. The campaign has assembled some 720 relatives of victims, all of whom believe the death penalty has amplified their grief rather than consoled them.

Deldelp Medina is one of them. Her aunt Magali was murdered eight years ago in a frenzied attack. To add to the emotional devastation of the event, the murderer was Manuel Medina, Deldelp's cousin and Magali's only son.

Manuel, a schizophrenic, was in the grip of a psychotic bout at the time he killed his mother. Prosecutors in Florida, where Magali was killed attempted to apply the death sentence to Manuel, and it took his family six years to fight the charges and have them dropped; Manuel is now being indefinitely held in a high-security mental hospital.

"The death penalty is emotionally draining for families like mine," Deldelp Medina said. "It consumes you and takes over your life – there has to be a better alternative where the perpetrators are put on life without parole."

Woodford said she had watched time and again as the families of victims began by being in favour of their loved one's murderer being executed, but had come over time to see it as a terrible burden. "This is an unbelievably painful system for families. There's no closure, there's no finality, it goes on for years inflicting so much harm and damage."

Should California vote yes next week it will become the sixth state in five years to repeal the death penalty. Connecticut abolished the practice in April, joining Illinois, New Jersey, New Mexico and New York. © Guardian News and Media 2012