A report warns the council is "now at a financial crossroads" which includes the possibility of making "drastic" cuts to other services in order to pay for spiralling numbers of children going into care.
It comes after analysis by the Local Government Association (LGA) showed councils up and down the country had overspent by a total of £770m on children's social care in 2018/19, which is expected to double to £1.4bn next year.
Last year Blackpool overspent by £5.4m on its total children's services budget.
This year an overspend of £8m is predicted in children's services, including nearly £7.8m in children's social care, which represents more than a quarter of the total children's services budget of £31.2m.
The main pressures are from the cost of looking after children in care, with numbers reaching 580 in June.
Nearly £4m has also been put into implementing an improvement plan after children's services was rated inadequate by Ofsted in December last year.
Council leader Coun Simon Blackburn said the spending was vital to ensure vulnerable children were properly cared for.
He said: "There is, necessarily, a financial cost of turning around a Children’s Services department.
"We will prioritise this funding, and ensure that our children have everything they need.
"There is a broader point however, that across England and Wales, over 95 per cent of councils are overspending in this area.
"That is because the Government does not fund these services adequately. I, and the LGA permanently lobby ministers and civil servants on this point, and it’s high time those voices were heard.”
In a report to the next meeting of the council's executive, director of resources Steve Thompson says "this pressure will be difficult to manage in-year using working balances and reserves".
He adds if such large overspends are repeated in future years without significant additional government funding, "the position will become impossible to reconcile against available resource."
Mr Thompson warns the council is "now at a financial crossroads" where the "unavoidable costs of children's social care" can only be met from sources including "drastic cuts to services elsewhere".
The only other options would be to spend the council's reserves, which will eventually dry up, or to attract significant external funding.
Additional costs this year are due to measures including recruiting additional social workers after Ofsted inspectors said some of the town's most vulnerable children were living in "chronic neglect".
A new structure has been introduced to enable social workers to spend more time with troubled families which it is hoped will eventually reduce the number of children in care.
While spending on children's social care nationally represents 18 per cent of total council spending, in Blackpool the proportion is much greater at 27 per cent.