The initiative is due to come into effect in July, however opposition to the plans is growing across the county as there are no doctors currently signed up to the scheme.
Local political representatives have accused the Government and the HSE of bullying the doctors.
Clonmel GP Dr Kevin Kelly there on the county-wide opposition to the plans to bring in free care for under 6's.
Doctors say they will not be signing up to the plan as the current infrastructure of their practices cannot cope with the increase in patient appointments that it would bring.
Dr Kelly says demand for GP services is already very high
North Tipperary Independent TD Michael Lowry says it's not just South Tipp doctors that are against the scheme, but North Tipperary GPs too.
While South Tipp's Mattie McGrath says the Government and the HSE are bullying the doctors into accepting the scheme by threatening to take away their current card-holder patients under 6.
Doctor Kevin Kelly says there are a number of issues that would have to be resolved before doctors would consider signing up to this scheme.