During a crunch vote at County Hall the entire Labour group, Liberal Democrats, Green Party and several independents all backed a bid for the authority to employ nobody at all from the spring.
In the end, 27 councillors from the controlling Conservative group had to team up to reject the motion, saying it would be “ludicrous” to agree to it.
Mrs Haines, who earns £176,000 a year, is retiring by May and adverts are currently out searching for a replacement, who will be paid £151,000 rising to £170,000 by 2017.
The opposition parties said due to unprecedented cuts at County Hall, with £98 million due to be slashed off budgets by 2017, they should leave the role unfilled.
Instead, the current chief executive responsibilities could be shared among the directors, given to leader Councillor Adrian Hardman, or handed to one director rewarded with a promotion.
It was laughed out by the Tories, who said the request could cause chaos and leave staff clueless about who was really in charge.
Coun Hardman said: “The reason I do think we need a chief executive more than ever is because we do live in extraordinary times, and that requires someone strong to be in charge.
“We did consider sharing a chief executive with another council but quickly discounted it because there was nobody we could see fitting in easily, and we also looked at the ‘great leader’ model, but I decided against that one as I suspect I haven’t the judgement or patience to pull it off.
“I struggle to think of any great organisations or companies who operate without a chief executive.”
Councillor Marcus Hart, the cabinet member for health and well being, said: “We need someone at the helm of an organisation which spends £300 million of public money on services in our county, the idea we could run without one is nonsensical.
“Do we have schools without head teachers, operations in hospitals with no surgeons, planes with no pilots? If you follow the logic through, where does it end?”
Councillor Tom Wells, from the Liberal Democrat group, said: “I wouldn’t normally propose something like this but we live in extraordinary times and are imposing draconian cuts on the most vulnerable members of society.”
Labour supported his bid to leave the role vacant and review it periodically, which was backed by all the opposition councillors, but it was defeated by just four votes.