Editor's note: The dramatic exoneration of falsely accused murderer Michael Morton is the subject of CNN Films' "An Unreal Dream, The Michael Morton Story," airing Thursday, December 5, at 9 p.m. ET/PT on CNN TV.
(CNN) -- Seth Penalver and Herman Lindsey are no longer on Florida's death row, but they are fighting for those who still are. Penalver and Lindsey, two of Florida's death row exonerees, held a press conference on Wednesday asking Florida Gov. Rick Scott to veto a death penalty bill recently passed by the state legislature.
If the bill is signed into law, 13 people could be executed in Florida this year.
The bill, referred to as the "Timely Justice Act," limits the appeals process and speeds up state executions.
"If the bill would have been in effect at the time of me being sentenced, I wouldn't be here talking to you today," said Penalver, who five months ago was acquitted on charges related to a triple murder. New evidence was uncovered years after he exhausted his original appeals, winning Penalver his freedom after 18 years behind bars.
"There's no ifs, ands or buts about it. You're going to put innocent men to death," warned Lindsey, who was exonerated after three years on death row.
One of the bill's sponsors, Florida Rep. Matt Gaetz, said the "Timely Justice Act" will not kill innocent people.
"We have more sophisticated juries today, a higher demand for forensic evidence," said Gaetz, "so I don't believe that keeping people around who have confessed to the crime, who weren't claiming their innocence, really serves the state that well."
The "Timely Justice Act" would mandate the governor sign death warrants in capital cases within 30 days after the Florida Supreme Court has completed its review. This is after the federal courts rule and the governor completes clemency proceedings, Gaetz said. The bill states that executions are to take place within 180 days of a death warrant being signed.
If the bill becomes law, the appeals process in death penalty cases will be shortened and limited. "Too often we have appeals that drag on regarding paperwork and production of records and effectiveness of one's lawyer, and those types of appeals are brought by people who have confessed," Gaetz said.
Gaetz said the bill will "enhance the deterrent factor of the death penalty," it will be a "tremendous help to victim's families" and it will cut down stays on death row to "below 10 years."
This bill has nothing to do with justice but more to do with politics, said Howard Simon, executive director of the Florida American Civil Liberties Union. "The premise of the bill is wrong. We don't have people sitting on death row for years," Simon said. "The average number of years is a year less than the national average." The national average for inmates on death row is 14 years.
Florida leads the nation in people sentenced to death and then exonerated, according to the Death Penalty Information Center. Penalver, the state's most recent exoneree, is number 24.
Penalver is asking for a meeting with Scott so he can show him his case files. Penalver said after showing him the evidence, he would ask the governor, "Would you kill me after reviewing this evidence? Would you sign this bill into law?"
Scott's office wouldn't say if he would be willing to meet with Penalver but it issued this statement, "We want to hear from Floridians about the merits of this legislation, which our General Counsel's office is currently reviewing."
The bill will be presented to Scott in June and he will have 15 days to decide whether to make the "Timely Justice Act" law in Florida.