LINCOLN, Neb. — There’s not a lot of sympathy for the 11 men on death row in Nebraska, but spurred by frustration about the growing difficulty and cost of carrying out executions, lawmakers are considering eliminating the death penalty.

If the Legislature outlaws capital punishment, Nebraska would become the first conservative state in more than 40 years to abolish the death penalty. Capital punishment opponents are optimistic following an initial vote this spring to repeal the law but acknowledge they still face a challenge as opponents led by the governor scramble to block the change. Another vote on the issue could come this week.

An unusual coalition of Democrats and Republicans has formed behind the repeal effort.

While Democrats cite racial disparities of who is sentenced to death and the possibility of executing an innocent person, Republicans point to the legal hurdles that have prevented the state from executing anyone. Nebraska’s last execution was in 1997.

“You always want to feel as a legislator that you’re sticking up for the victims,” said Republican Sen. Colby Coash, who said the death penalty wastes tax money and makes a false promise to victims’ families. “I don’t speak for the victims, but how is it justice if a state imposes a sentence that it’s never going to carry out?”

The last conservative state to abolish the death penalty was North Dakota in 1973. In the past six years, four more liberal states have ended capital punishment: New Mexico in 2009, Illinois in 2011, Connecticut in 2012 and Maryland in 2013. Thirty-two states still have death penalty laws.

Some legal experts believe a repeal by Nebraska could prompt other states to consider the move, especially those that rarely execute people.

“If New Hampshire wanted to abolish the death penalty, Nebraska could set a terrific precedent,” said Frank Zimring, a law professor and death penalty expert at the University of California, Berkeley. “But it probably wouldn’t work in Texas or Missouri.”

Nebraska’s debate shows the topic no longer is a “third rail” issue among conservatives, Zimring said.

Efforts in Nebraska to carry out executions have run into repeated roadblocks. In 2008, a state Supreme Court ruling outlawed the electric chair. Then, after Nebraska switched to lethal injections, the slow process of inmate appeals prevented executions for so long that the state’s supply of sodium thiopental expired and officials couldn’t restock its reserve.

Since Nebraska reinstated the death penalty in 1973, only four inmates have been executed. One inmate has been on death row for 35 years.

Capital punishment opponents pointed to an ACLU-sponsored study this year by Seattle University that found capital cases in Washington state cost about $1 million more than first-degree murder cases where prosecutors didn’t seek the death penalty.

In March, the Legislature voted 30-13 to repeal the death penalty, but lawmakers must vote on the issue twice more and Republican Gov. Pete Ricketts has promised a veto. The 30 votes are enough to overcome a veto, but 33 votes are required to defeat a filibuster that could kill the bill.

Death penalty supporters said they’ll do whatever they can to retain capital punishment and execute those on death row.

“I wouldn’t expect the debate on this to be short,” said Republican Sen. Beau McCoy, who supports the death penalty. “If it were to get that far (to a veto override), I think you’ll see some high-stakes drama the likes of which hasn’t been seen in this building in quite some time.”

McCoy said he’s confident most Nebraskans support the death penalty, regardless of the state’s inability to impose it.

“The ones who are on death row now deserve to be there,” McCoy said.

This is the closest Nebraska has come to ending capital punishment since 1979, when Gov. Charles Thone vetoed a repeal measure. A recent Pew Research Center study found 55 percent of Americans favored the death penalty, down from 62 percent in 2011.

Miriam Thimm Kelle started lobbying Nebraska lawmakers a decade ago to abolish the death penalty after a long legal fight over the man convicted in 1985 of torturing and killing her brother.

“When we started out, no one in the Legislature wanted to talk about it,” Thimm Kelle said. “They just pointed to the worst of the worst and said, ‘Get rid of them.’ But I think now they’re realizing it isn’t healthy for victims’ families to have to wait 30 years.”