Somerset County Council has been talks with the unions over the move, which it said could save £1m over a two-year period.
The proposals come after an external audit report on the authority found it could run out of money in the next two to three years.
Unite has said it will recommend its members reject the plan when it is put to the workforce in a ballot next month.
Steve Preddy, Unite acting regional secretary, said: “If [the council] had taken the advice of its financial advisors and raised council tax in line with inflation in recent years, the budget would now be running a surplus.”
Preddy called the proposals “a step too far” and added: “Unite, along with other local government unions, will be resisting this mean-minded move.”
In July, the council’s chief accountant Lizzie Watkin denied suggestions that the council was close to issuing a Section 114.
A council spokesperson said: “Staff have not been asked to take two days unpaid leave, however we are in dialogue with unions to achieve a saving and have suggested two days unpaid leave over the Christmas period as a temporary two-year measure to meet that target.
“Austerity is a big challenge for local government, especially for councils with responsibility for vulnerable adults and children, which account for two-thirds of our budget.”
An external audit report by Grant Thornton, from July, cast doubts over the council’s financial resilience.
The report said: “The inability of the authority to deliver against its budget is now pervasive to the whole authority and without urgent actions could result in it running out of money in the next two to three years.”
Grant Thornton found that only £11.1m of the budgeted £19.5m of savings were delivered in 2017-18.
The council’s financial problems were due to “continued overspending, predominantly in the area of children and families”, the audit report said.
As reported in PF last week, concerns have been raised financial difficulties will mean multiple councils will struggle to continue to deliver statutory services, including for vulnerable children.
