The latest bill on the issue is sponsored by Democratic Rep. Reuven Carlyle of Seattle, who doesn't expect it to pass this year but says it will spur further debate at a time when public attitudes about capital punishment are changing.
"We are in the midst of a profound shift in thinking, in large part because of the impact of DNA testing," he said. "I believe the public is undergoing a rapid transformation in their view given the fact that we have repeated headlines about injustices in terms of the wrongly convicted."
The death penalty is currently used by the federal government and 33 states. Seventeen have abolished it, with Connecticut being the most recent last year, though its ban only applies to new cases.
A death penalty statute is still on the books in Oregon, but Gov. John Kitzhaber stopped an execution in 2011 and declared no one would be put to death during his time in office.
Several other states have introduced measures this year, including Nebraska, Montana and Maryland, according to the National Conference of State Legislatures. The Maryland state Senate is expected to vote Wednesday on its measure.
Carlyle's bill to end capital punishment in Washington also will receive a public hearing on Wednesday before the House Judiciary Committee. It's co-sponsored by 20 other lawmakers, including one Republican, Rep. Maureen Walsh of Walla Walla.
The last execution in the state came in September 2010, when Cal Coburn Brown died by lethal injection for the 1991 murder of a Seattle-area woman. After spending nearly 17 years on death row, he was the first Washington inmate executed since 2001.
Since 1904, 78 men have been put to death in Washington. Eight men are now on death row at the state penitentiary.
A coalition known as Safe and Just Alternatives was formed in 2011 to try to have the death penalty abolished in the state. Mishi Faruqee, the group's campaign manager, said that over the past year, it has been focused on community outreach on the issue.
Faruqee believes momentum is building in the state, even though bills introduced in past years to abolish the death penalty have not garnered much support.
"Given the budget shortfalls that Washington state is having, ending the death penalty is a very clear way for the state to save money," she said.
Death penalty cases cost about $470,000 more to prosecute and defend than aggravated murder cases that don't involve the death penalty, according to a 2006 Washington Bar report. On appeal, costs average about $100,000 more for death penalty cases than for non-death penalty cases.
Spending has become a key issue for lawmakers, who are in the midst of a 105-day legislative session aimed at patching a projected $1 billion deficit for the two-year budget ending in 2015. The figure does not include a court-ordered requirement to get more money into the education system.
Still, Sen. Mike Carrell, R-Lakewood, chairman of the Senate Human Services & Corrections panel, opposes any discussion of abolishing the death penalty.
"When I ask myself, what would the victims think justice is, I know what the answer is," he said. "The death penalty is appropriate for extreme cases."
A companion bill in the Senate hasn't received a public hearing this session. Republican Sen. Mike Padden of Spokane Valley, chairman of the Senate Law & Justice Committee, wouldn't say why, and he didn't want to talk about his thoughts on the death penalty unless the House measure advances and is sent to his committee.
The Washington Association of Prosecuting Attorneys is split on the issue and hasn't taken a position on the latest bill.
"We do defend the constitutionality of the current statute and how it has been applied in Washington state," Tom McBride, executive secretary of the association, wrote in an email. "The moral question as to whether to have a death penalty is appropriately decided by the Legislature."
The death penalty abolition bill is House Bill 1504.