The warning comes after a major row erupted between the Scottish Government and local authorities over how much the scheme will cost.
Ministers argue the move to deliver 600 hours of childcare to two-year-olds from workless households will require capital funding of about £61 million.
However, Cosla, the umbrella body for Scottish councils, argues the real figure is closer to £114m.
Giving evidence to the Scottish Parliament's finance committee yesterday, Education Secretary Michael Russell said he did not agree with that figure.
"The Cosla figure is very substantially higher, but we have moved from early discussions of a lower figure," he said.
"We will continue to discuss it, but we are confident in our robust calculations. Of course, there will be flexibility, but I think these calculations are very robust indeed. Cosla has talked about £114m, but we don't agree with that figure for reasons we have also given to Cosla."
However, after the committee meeting a Cosla spokesman launched an outspoken attack on Mr Russell. "The fact that we are in this position reinforces our concerns on delivery prior to the start of term in August - a point which we will be making to the education committee in the strongest possible terms later this month," he said.
The spokesman also attacked comments by Mr Russell that he was ready to negotiate with Cosla.
The body has previously criticised the Education Secretary for failing to consult over changes to rural school closures, and earlier this year accused the Scottish Government of underfunding a commitment to introduce universal free schools meals to primary pupils by £25m.
"We have a number of difficulties with this, the first being that Mr Russell has form for talking about a negotiation with councils while not delivering on it - a perfect example being his recent stance on rural schools," the spokesman said.
"We have learned from previous dealings with him that his actions do not always match his words. That is why, if I am being honest, his meagre assurances around this policy do not cut any ice with us."
Scottish Conservative finance spokesman Gavin Brown said: "The Scottish Government has clearly not thought through how this childcare policy will be implemented in August. It has taken five months for the Education Secretary to produce a capital figure, yet now he is admitting it could rise even further by many more millions of pounds.
"With just eight weeks until this key SNP policy is due to be implemented, it's staggering they cannot provide a cast-iron guarantee the buildings and facilities needed will be ready in time. Parents looking on at this ineptitude will rightly wonder whether their child will actually get the childcare promised by the SNP."
A Scottish Government spokesman said: "We are committed to investing £280m over two years to expand funded early learning and childcare for three- and four-year-olds - from 12.5 hours to almost 16 hours a week - from August, and to extend this entitlement to the 27 per cent most vulnerable two-year-olds, reaching about 15 per cent in the first year."
Local authorities in Scotland have a statutory duty to provide three- and four-year-olds whose parents wish it with a minimum of 475 hours per year of funded pre-school education.
Before 2007 the annual entitlement was 412.5 hours, and this will rise to a minimum of 600 hours from August under provisions set out in the recently passed Children and Young People Act.
The Scottish Government is also expanding this entitlement to vulnerable two-year-olds.