Their proposed changes, outlined by Assemblywoman Amy Handlin (R., Monmouth), a member of the committee investigating the lane closures, include establishing a single chain of command at the Port Authority, whose top appointees now owe their allegiance to either the New York or the New Jersey governor.
The proposals also call for an independent monitor with subpoena power to oversee the agency, and requirements that top agency officials file detailed financial disclosure forms to be posted on the agency's website.
In addition, Republicans would make it a crime to use "one's official position to hurt commuters for unofficial purposes," punishable by jail time of up to 18 months and a fine of up to $10,000, according to a document outlining the proposals.
Other bistate agencies include the Delaware River Port Authority, with commissioners from Pennsylvania and New Jersey.
Bramnick said Republicans had not spoken to lawmakers in neighboring states about introducing similar measures. He said he would share the proposals with the cochairs of the legislative committee investigating the lane closures, Assemblyman John S. Wisniewski (D., Middlesex) and Sen. Loretta Weinberg (D., Bergen).
Wisniewski said Thursday that he had not seen the proposals, but he suggested they were premature.
"With all due respect to Leader Bramnick, it is he and his colleagues who continually inject partisanship into this investigation. They've made it clear they have no interest in finding out how this abuse of power happened," Wisniewski said.
"You can't begin to intelligently prescribe a solution until you know the full extent of the problem," he said.
The Port Authority's operations have come under scrutiny in light of the investigations into the September lane closures by lawmakers and federal prosecutors. The closures jammed traffic in Fort Lee over four days in September.
Gov. Christie fired an aide and dismissed a political adviser last month after e-mails revealed an apparent plot to create gridlock.
The aide, Bridget Anne Kelly, sent a former Port Authority official an e-mail that read: "Time for some traffic problems in Fort Lee." Christie has maintained tat he played no role in the lane closures, which some have alleged were political payback to the Democratic Fort Lee mayor for failing to endorse the governor for reelection.
On Thursday, Kelly and the dismissed adviser, Bill Stepien, were ordered by a court to defend their position that they are not required to turn over documents in response to legislative subpoenas.
The legislative panel went to court Wednesday to force responses from Stepien and Kelly, who have invoked their Fifth Amendment rights against self-incrimination. Hearings in the case are to be held March 11 in Superior Court in Trenton, under orders issued Thursday by Judge Mary Jacobson.
Republicans said their proposals would also apply to other state authorities - "everything from parking authorities to housing authorities," said Assemblyman Michael Patrick Carroll (R., Morris).
A Christie aide who served as the governor's liaison to the Port Authority was recently named to a high-level position at the agency, the Newark Star-Ledger reported this week.
Nicole Crifo - who has received a subpoena from lawmakers - will serve as chief of staff to Deborah Gramiccioni, the new deputy executive director Christie named to the Port Authority, according to the report.