The schools also oppose the bill's provisions on athletic transfers. Under NCAA rules, an athlete's school can block his or her release to another school. Athletes who transfer without permission are unable to receive scholarships or compete for one year.
Padilla's bill would require the schools to approve all transfer requests without restrictions.
The opposition letter from affected universities said this provision would make athletes "desirable prey."
"It creates a competitive disadvantage for the schools that would be impacted by the bill," Dunkley said. "Every other school can make a decision on whether they want to allow transfers. It would make our four schools the only ones with this requirement."
But Huma said the proposal will prevent students from being "held hostage when they want to transfer" and athletes from being held to different standards than other students.
Padilla added that "a student athlete is a student first" and should be able to transfer without penalty.
David Ridpath, Ohio University assistant professor of sports administration, said the change in transfer rules may actually help the schools with recruitment.
"The schools in California will have the ability to recruit people saying that 'hey we won't restrict you,' " Ridpath said. He added that the guarantee of a scholarship regardless of performance and the ability to change schools easily will make the four schools a desirable place for athletes.
The bill has won support from one group of student athletes. Jeff Locke, the kicker for the UCLA football team, coordinated a petition in favor of the bill signed by 72 current UCLA football players.
"I just felt like the lawmakers needed to know that there are players behind this bill even if the school many not be," Locke said.
The bill passed 22-14 in the Senate and is scheduled for the Assembly Higher Education Committee June 27.
"It creates a competitive disadvantage ... It would make our four schools the only ones with this requirement."