Burns decided this week to call it quits at the end of June.
Many assumed he decided to leave, because of talk by the new school board majority about undoing the diversity policy in favor of neighborhood schools.
But Burns came right out and said, "ensuring that the board's policies are implemented as they wish and for me, that's not something I'm comfortable doing, given the direction of the policies."
Now a number of supporters of the new board majority are calling Burns insubordinate.
"If he doesn't think that he can administer those policies, and clearly he doesn't, then he needs to go and he needs to go now - however they do it - whether he is fired, whether he goes ahead and leaves," said Dallas Woodhouse with Americans for Prosperity.
One member of the new majority stopped short of using the same terminology.
"I wouldn't necessarily use that word, uh, 'fire'," school board member John Tedesco said. "He's already announced his resignation so, you know, we might just have to see what's the best way to move forward now knowing we have a superintendent who has publicly stated that he cannot do his job."
But Tedesco refused to rule out firing Burns.
"I think all things are on the table at this time now," Tedesco said. "Our attorneys are going to have to work with the Board of Education in talking about this now as a private personnel matter."
A former long-time chairman of the school board, says supports the school's current diversity policy.
Republican Cary real estate agent Bill Fletcher says he thinks for the good of students it's time to quit throwing bombs and start talking about the reality of the changes planned by the new majority.
"I think it's heading in the wrong direction based on what I know about it today," Fletcher said. "But put a budget to it, tell me what happens to the state funding for our bus routes. Tell me, if there's complete openness, what happens to the funding formulas that the system has been relying upon to provide the budget. None of that work has been done to my knowledge. And to ask the senior people who know those numbers that know the implications, to exit at this point just doesn't make any sense."
A school board meeting will be held Tuesday to discuss Burns' future with attorneys; it will also be closed to the public.
If the board decides to fire him, they would have to pay his salary through June.