Teaching unions have been outraged, and the move also drew strong criticism from the Office for Standards in Education in a second critical report on the local education authority in 18 months. Some national commentators said the referendum was irresponsible.
Now, with 23 of the council's 70 seats up for re-election on June 7, Labour may lose control of Bristol, where it currently has an overall majority of only two.
Lifelong Labour supporter Paulette North, assistant secretary of the National Union of Teachers in the city, certainly believes, and hopes, so.
She said: "This has been a public relations disaster for the Labour party. The three largest teaching unions have put in a jont motion of no confidence in the Labour administration, and I think parents are quite sympathetic to our cause.
"I'm not going to be voting Labour, and I don't think that Labour will get in here. I think it will be a hung council."
In fact, the impact of the cuts has been reduced after the council managed to find pound;2m from selling its shares in Bristol Airport. In addition, Ms North said headteachers were doing all they could to avoid staff cuts, and there had not yet been any compulsory redundancies.
Donald Shell, senior lecturer in politics at Bristol University, said he thought Labour might get off the hook. The fact that ways had been found to limit the cuts meant Labour could avoid punishment at the polls.
He said: "The Labour party acted completely irresponsibly in refusing to stick to its own plans not to cut services. In reality, the cuts were not as bad as predicted.
"But that can only increase the public's lack of trust in politicians: they threaten cuts, but then do not make them."