Under the Scottish Government policy local authorities were expected to offer 600 hours of childcare to two-year-olds from workless households by August this year.
However, a survey by the Scottish Conservatives shows many councils do not currently have the required capacity, with private nurseries also struggling to offer sufficient places.
A new legal duty requiring councils to implement the policy by August has already been postponed and will now not come into force until the end of October.
There has also been conflict over how much the policy will cost, with the Government estimating capital funding of about £61 million and Cosla, the umbrella body for Scottish councils, arguing the real figure is closer to £114 million.
In response to a freedom of information request by the Scottish Conservatives Angus, Midlothian and Moray councils said they had no spare places within council nurseries.
Aberdeen's nurseries are all full with significant waiting lists, meaning two-year-olds will instead be sent to family centres currently used for children referred by social work or health visitors.
Edinburgh said it will be October before it finds places for those young children eligible while South Lanarkshire stated there was "limited capacity" in council nurseries adding private providers will not be offering places.
Scottish Conservative young people spokeswoman Liz Smith said: "The SNP rushed out this policy in January and, now, eight months later, parents still have no idea how many of these eligible two-year-olds will actually receive free childcare and how much it will cost.
"The Scottish Government has ordered councils to deliver on this policy, but it is very clear that several are struggling to do so.
"Councils simply do not have enough places or sufficient accommodation.
"Parents in some of the poorest households in the country have now been left worrying whether their two-year-old will actually get the childcare promised to them."
A Scottish Government spokesman said it had committed at least £280 million over the next two years and was working with local authorities to deliver a "sustainable and ambitious" expansion.
He added: "Local authorities have confirmed they are on track to extend the provision from August.
"In exceptional circumstances, where this is not possible, councils will ensure eligible two-year-olds receive a place as soon as possible in the period up to October 31."