But the parents regard Lingle as the main obstacle.
Friday's citations came about an hour after the parents had finished a news conference and most reporters and television cameras had left the lobby of the governor's office, where the sit-in has been conducted nonstop since Wednesday afternoon.
Clare Hanusz, a member of the ad hoc parents group Save Our Schools, said seven adult demonstrators were handed the citations by a uniformed state sheriff's deputy. The handful of children also present weren't cited, she said.
A plainclothes deputy, whom she identified as Bryan Marcial, told the cited parents that they could resume their sit-in during the day next week but they risked arrest if they tried to remain in the lobby past closing hours, Hanusz said.
The fifth floor of the state Capitol, where the offices of Lingle and Lt. Gov. James "Duke" Aiona are located, is usually closed to the public after 4:30 p.m. on weekdays.
"It feels like they're kind of toying with us," said Hanusz, a Honolulu attorney who has a son and a daughter in public school. "We had a lot of media here at 4 o'clock. They waited until about 5:30 p.m. to inform us that this decision had come down."
Lingle's office released a statement late Friday that said: "Individuals who are making false allegations against the governor should encourage the Hawaii State Teachers Association to change its position that it will no longer negotiate to end the school closures."
Hanusz said Marcial first told them the decision to issue citations came from the state sheriff's office, but later said the decision had been made by the governor's office.
The cited parents were told they are to appear in court on May 5. But one of those parents said she remained in good spirits, as five adults and three kids prepared to continue the sit-in Friday night in the lobby.
"We're going to go forward because we think that's what it takes," said Lois Yamauchi, 46, a University of Hawaii education professor whose two sons attend public school. "If that's how they want to treat us, we'll respond the way we think is most appropriate."
The parents have demanded that Lingle personally participate in the furlough negotiations. They also want an agreement to be reached by mid-April.
On Thursday, Lingle said in a statement she has personally met with all the negotiating parties, and called claims by the parents that she hasn't "patently false."
Lingle added: "Occupying government offices will not create additional revenues to end the school furloughs and impedes the ability of the general public to conduct business with the state."
That last assertion irked Marguerite Higa, a parent and spokeswoman for Save Our Schools.
"She says that we're impeding important public business," Higa said at Friday's press conference. "This is public business. I mean, we're parents, concerned aunties, uncles and children. We're the public too. We have important business. We want to restore school days for 170,000 of Hawaii's school kids."
The parents plan to continue the protest on Monday. But they said they'll move it on Saturday to a spot fronting Washington Place, once the official residence of Hawaii governors but now a museum.
Parents have also scheduled a rally at the state Capitol grounds on Sunday.