Devon CC has imposed a recruitment freeze as it grapples with an £8.1m overspend this financial year.
The projected total arises is mainly from an extra £6.4m spent on adult social care because of increased demand, the council said, with 10,422 care packages in place for elderly people - 584 more than budgeted.
In addition to the recruitment freeze, employment of temporary staff, agency staff or consultants has been banned other than with the permission of chief executive Phil Norrey.
The only exceptions will be front line social workers and other posts where a vacancy would leave the council unable to meet statutory responsibilities.
Deputy leader John Clatworthy (Con) said: “We have absolutely no intention of not balancing the books.”
He cited pressures from increased demand for care from those aged over 85 and the national living wage for care workers and said many other councils were in a similar position.