The Scottish Government initiative came under fire after The Herald highlighted hundreds of families struggling to access free places.
The SNP promised 600 hours of free nursery education for parents of three and four-year-olds across Scotland.
Councils deliver the policy by using part of their block grant to provide enough free places in state nurseries - or by paying partnership providers in the private sector if they cannot meet the demand themselves.
However, a survey by parents from Glasgow has shown hundreds of children unable to secure the places at the private nurseries they currently attend. Families in East Lothian are also hit.
The Scottish Conservatives said the policy failure was "indicative" of the SNP's approach on childcare issues. Liz Smith, the party's spokeswoman for young people, said: "Not only is this a matter of deep concern in terms of our children's future education, it is also more evidence that the wild promises made by the SNP to parents are not being delivered."
Kezia Dugdale, education spokeswoman for Scottish Labour, said: "This is further evidence the SNP's plans for childcare are half-baked and more concerned about headlines than details."
A Scottish Government spokeswoman said: "While we expect local authorities to meet their statutory responsibilities, clearly it is for each of them to decide how best to do that."