On Tuesday, state Senate President Stephen M. Sweeney (D., Gloucester) announced that he was introducing the bill to abolish the board of trustees, saying it brings too many people into decisions, makes it difficult to get things done, and "waters down accountability."
Gov. Christie said he supported the idea of changing the university's governing structure.
The proposal came on the eve of Rutgers' absorbing most of the University of Medicine and Dentistry of New Jersey.
It also came on the heels of an embarrassment earlier this year when Rutgers basketball coach Mike Rice was fired after a video was made public showing him berating players with gay slurs and hitting and kicking them.
Some lawmakers blamed university officials for not ousting Rice more promptly.
Other controversies followed, including allegations that newly hired athletic director Julie Hermann had herself verbally abused student players when she was at the University of Tennessee.
But almost immediately after Sweeney made his proposal, protests came from Rutgers, with academics accusing politicians of an illegal power grab.
The board of trustees dates to 1766, when the university was established through a charter from England's King George III. In 1956, the board became largely advisory when the state took over the previously private university and established the board of governors.
The board of governors has 11 voting members - five appointed by the trustees and six nominated by the governor and approved by the state Senate.
The trustees have 59 voting members, most of them appointed by the board itself.
On campus, there are worries that eliminating the trustees would make the university too easily controlled by politicians.
"Even universities as large and ancient as Rutgers can be fragile institutions whose reputation and legitimacy can be easily diminished if not protected against the ebb and flow of political tides," university law professors Ronald Chen and Robert Williams wrote in a letter to lawmakers.
They also warned that because the Legislature did not establish the board, it cannot legally abolish it.
Lawmakers decided not to vote on the matter this week, and the board of governors, in an emergency meeting Friday morning, did not take any formal action.
But Tom Hester, spokesman for Assembly Speaker Sheila Oliver, said Oliver believed "a reexamination of the university's governance structure may be warranted" and was considering having committee hearings to work on the issue in July.
Lawmakers have also introduced a plan to appoint a commission to study Rutgers' governance with the requirement that it make recommendations within six months.