Staffordshire County Council was due to receive the NHS funding to pay for services for elderly and disabled people.
But council chiefs say NHS England then asked them to cut delays moving patients out of hospital and into social care by two thirds over an eight-week period.
The authority failed to meet the demands, which bosses say were made at "extremely short notice."
Now the council claims NHS England has threatened to withdraw the much-needed cash.
It is lobbying the Government, while making contingency plans with clinical commissioning groups to deal with any shortfall.
It comes after the council had to make cuts in areas such as drug and alcohol services after the NHS withdrew £15 million last year.
Council leader Philip Atkins said: "As a county council we will spend a record £300 million on health and social care this year and the money from the NHS Better Care Fund is vital to support the most vulnerable in our communities at home this winter.
"If the money is withheld, we, like other authorities in the same position, have made it clear that there could be a profound impact on health and social care and actually increase the pressure on the NHS."
Bed blocking can occur when patients are medically fit, but cannot be discharged from hospital due a lack of available social care.
The county council is one of 18 authorities across the country which failed to hit targets to reduce the problem.
Alan White, cabinet member for health, care and wellbeing, said: "We remain committed to working with the local NHS to achieve targets set by NHS England and we will continue to work with CCGs to try and ensure that essential services can be funded."
NHS England was contacted but declined to comment.
The county council's cabinet will meet on Wendesday, October 18 to examine how the £19.5m shortfall could be met if the BCF funding is not forthcoming.