Almost 1,200 jobs are set to be cut by Hampshire County Council after it approved £55m of savings.
The council employs 15,000 people so the cuts represent 8% of the workforce.
The Conservative-led authority has blamed the cuts on a reduction of £30.9m (14.3%) in its government grant, following the Spending Review.
It insists it cannot yet say what its four year saving target is, but opposition councillors estimate it to be about £100m.
Hampshire County Council wants to reduce the number of children's centres from 81 to 53, focusing services on more deprived areas.
'Tears in eyes'
The council is planning to move from the existing model of 81 individually managed children's centres to a total of 53 merged centres, in a bid to save £6m.
In the vast majority of cases there will be mergers of management and services and will not involve the closure of sites or buildings.
The children's centre consultation is open until 14 March.
Mother Catherine Ovenden broke down in tears as she was allowed into the chamber to make a plea to protect children's centres.
Liberal Democrat councillor Keith House said: "It was a very moving moment there were tears in a number of people's eyes including mine as a grandparent and parent."
The council argues it is a reorganisation that will not close centres and targets those most in need.
It has made some concessions with £1m being returned to a project for disabled children and concessionary bus fares now starting from 0900 GMT not 0930 GMT.