But Watson, who is beginning his second term in the Senate, said he wants to avoid "a knee-jerk reaction" in dealing with the backlash from Barbour's controversial pardons that have garnered national attention.
"I will spend a lot of time studying this issue to make sure we get it right," said Watson, who said he did not want to push through a change that "five or 10 years from now we are asking why did we do that?"
He added, "Any time you amend the Constitution, it is a big deal. You want to make sure you get it right."
At a Friday news conference, Barbour said, "I am very comfortable and totally at peace" with the pardons and said it would be a mistake to limit the authority of the governor to grant them. Barbour, whose tenure ended Tuesday, pointed out the U.S. Constitution gives the president the same authority on the national level.
He said he is opposed to "taking away from the executive the opportunity to give people hope and the opportunity to do better."
New Gov. Phil Bryant has been reluctant to comment on his fellow Republican's actions, but confirmed that he had met with Watson to talk about possible constitutional changes and indicated that he might support altering the governor's ability to grant pardons.
Bryant actually will have no role in any change other than the power of the bully pulpit. A change to the state Constitution requires approval of two-thirds of the members of both legislative chambers and approval of the voters. The state Constitution also can be changed through the citizen-sponsored initiative process.
The state Constitution gives the governor "the power to grant reprieves and pardons," though the person seeking the clemency must notify the public through a newspaper announcement that the pardon is being sought.
Democratic Attorney General Jim Hood has convinced a Hinds County circuit judge to at least temporarily halt the pardons to ensure that the fact they were being sought was announced in the newspaper.
Barbour said that of the 215 pardons and suspended sentences he granted, 189, or almost 90 percent, already had completed a sentence. By receiving the pardon, Barbour said the convicted felons would be more likely to find a job and be able to vote and hunt.
But Barbour's pardons will result in 26 felons being released from prison unless the courts ultimately find those convicts did not provide the proper notice. Five (four murders and one robber) already have been released, though they have been ordered to prove to the court they provided the proper notice in newspapers where their crime occurred. Those five served as trusties at the Governor's Mansion. Barbour has said that it is tradition for the governor to pardon Mansion trusties who perform well.
Barbour used the trusty argument in 2008 when he suspended the sentence of Michael Graham, who was convicted of stalking and finally shooting to death his ex-wife in 1989 on a Pascagoula street. Before leaving office, Barbour granted Graham a full pardon - in essence giving him a clean criminal record.
After that incident in his hometown involving Graham, Watson filed legislation to prevent a violent offender or sex offender from serving as a trusty. That legislation and other similar proposals have been killed in recent years.
House Democrats plan to introduce legislation this session to put safeguards in place while not stripping the governor of pardon powers.
As far as constitutional options, Watson said they include taking away the pardon power and giving it to a board, establishing a board and making the governor a voting member of it, establishing a board and allowing the governor to act only on the recommendations of the panel, stripping the power to pardon certain categories of violent offenders.
Watson said he does not support stripping the governor of pardon powers.
Because of the public outcry, Watson said he believes whatever the Legislature adopts will be approved by voters. But Sen. Willie Simmons, D-Cleveland, a former chair of the Corrections Committee, said, "I don't think we should change the law ... We should not take away options from the governor."
Simmons said it would not be wise to change the law because of issues related to one batch of gubernatorial pardons.
Bryant said he would use the power only when there is proof "beyond a reasonable doubt," such as DNA evidence, that the legal system had made a mistake and an innocent person had been convicted. He also said he would end the practice of trusties living at the Governor's Mansion. He said they will be used to perform certain duties to hold down the cost to taxpayers, but they would not be permanent residents.