"We've had a handful of incidents that have not cast Rutgers in a good light," Sweeney said.
With the University of Medicine and Dentistry of New Jersey slated to merge into Rutgers on Monday, it is important to streamline the university's governing structure, Sweeney said.
Under two boards, "there's too many excuses when things go wrong," Sweeney said.
The text of the bill - introduced last week - was unavailable Monday. Rutgers officials, saying they had not seen the proposal, said the university would fight to keep the board of trustees.
"Rutgers will vigorously oppose any legislation that violates the legislative contract established in the 1956 Rutgers Act," which requires that both boards of governors and trustees consent to any change in the university's governance, school officials said in a statement.
The board of trustees, which governed Rutgers from its founding as Queens College in 1766 until its reorganization under the board of governors in 1956, "is one of the oldest governing bodies in higher education in the nation," school officials said. "Indeed, it predates the nation itself.
"Moving precipitously to alter the legislation that created the board structure is unwarranted," school officials said.
The board of governors - with six voting members appointed by the governor and five elected by and from the board of trustees - has primary control over the administration of the university. It was not immediately clear who would pick the five if the board of trustees was abolished.
The board of trustees has an advisory role, though it retains responsibility for assets that belonged to the university before the 1956 reorganization.
The trustees last year protested a proposed merger of Rutgers-Camden and Rowan University, threatening to sue if the state moved forward with the measure - backed by Sweeney and other lawmakers - without their approval. The Legislature passed a restructuring of the university system that let Rutgers retain control of the Camden campus.
Sweeney denied that his bill was a reaction to the board's opposition.
"Look, it's 2013. It's time to move forward," he said. He said having two boards to govern one school "makes no sense."
"If we care about Rutgers - and we do care - we only should have one board, and that board should manage Rutgers University," he said.
Contact Maddie Hanna at 856-779-3232 or firstname.lastname@example.org, or follow on Twitter @maddiehanna