Further cuts to public services totalling £14m are being considered by Somerset County Council.
An email seen by the BBC shows the council is preparing to make cuts to 110 services by April 2019 and closing Taunton's park and ride sites.
Conservative council leader David Fothergill has not confirmed this figure but said the council was facing "considerable pressure".
If the cuts are made, this brings the total savings for 2017-18 to £28m.
This email was sent to Liberal Democrats following a meeting between senior members of the party and the council's chief executive, Pat Flaherty.
The Local Democracy Reporting Service said Mr Flaherty stated in July that 80 per cent of these previously identified savings have already been delivered.
Of the £14m in cuts needed, £4m will come from each of children's services, adults services and economic and community infrastructure (ECI), which includes highways maintenance and the council's contribution to the Somerset Waste Partnership.
The remaining £2m will be sourced from other projects and could also impact library services.
These cuts would have to be additional to £14m previously agreed for this financial year.
Closing Taunton's two park and ride sites would save the council £140,000 a year as the service is subsidised.
If the extra cuts are agreed, council services will be reduced to a core where only basic statutory needs are met.
One source within the Lib Dem group has also claimed the council's flagship capital programme of delivering 24 new and replacement schools by 2023 will not be achieved because the council cannot afford to service the £120m loan it would need to borrow to fund the design and construction.