Senate Judiciary Chairman Rey Graulty concurs, although he sees the danger more in terms of unsavory people who could threaten late-working legislative staffers.
But Senate Ways and Means Chairwoman Donna Ikeda and former Senate Republican leader Mary George, who once fought off an attacker when she was leaving the Capitol one night, disagree.
"Honey, if I can handle it, they can handle it," said George, now 79, recalling the 1988 incident in which she battled a 22-year-old escaped prisoner.
George and Ikeda said that with the state facing a $200 million budget shortfall, the $262,000 that would be spent for the salaries and equipment for the additional Capitol security officers could best be used elsewhere.
Ikeda said she has "a hard time" with Souki's proposal because the new positions would be a continuing expense, adding to fixed costs.
"Under the circumstances, I tend to believe that if we add money for security, I would rather see it go to the Judiciary. They have a bigger problem - that's not to say we don't have a problem," said Ikeda, who has received threatening phone calls.
"But I believe we can call in the police, as we've done in past, if we have to. I think we have enough of a security force."
There are 27 deputy sheriffs assigned to provide security at the Capitol and other government buildings in the Capitol District, said Henry Festerling, protective services administrator of the Department of Public Safety.
George, who ended 26 years in elective office when she retired 15 months ago, said she believes security at the Capitol is better than at most shopping centers.
On the night of July 22, 1988, George suffered cuts to her right arm and a bruise under her right eye when she successfully fought off an escaped prisoner. The prisoner eluded police who had taken him to the Queen's Hospital emergency room and was trying to get into George's car as she was driving away from the Capitol.
Graulty, who received a death threat when he was pushing gun-control bills two years ago, said he's recommending that his panel approve Souki's measure.
Graulty noted that two years ago then-Health Director Jack Lewin was punched in the face before a hearing on gun-related bills and that recently a demonstrator at the Capitol had to be subdued after he slammed into and spat on national anti-abortion activist Randall Terry, who was in Honolulu to lobby against legalizing same-sex marriages.