Ms Hutt was challenged by the National Association of Head Teachers Cymru to provide a simple breakdown of the money to be pumped into the initiative over the next three years.
At a recent meeting of its funding committee, association members voiced concerns that special educational needs pupils and education generally could also suffer as schools diverted staff to make up numbers for the FP when it is rolled out to all three to five-year-olds next September.
NAHT Cymru director Anna Brychan said members still had no idea how much money schools would have to bed down the learning strategy, with many feeling it would prove an impossible task.
"Jane Hutt has repeatedly assured us that the programme is fully costed and that the resources are available," said Ms Brychan.
"If the minister is confident that the money is there, then in the interests of transparency we ask that she publishes urgently details of the funding that has been made available for the FP every year for the next three years. And please can she also tell us how she means to distribute it."
Last week Ms Hutt faced united condemnation from local government and from Welsh teaching unions over the amount of education funding outlined in the draft budget up to 2011.
One union, the NASUWT Cymru, is also threatening strike action and a hijack of all major initiatives if more money for schools is not found.
Meanwhile, the Welsh Local Government Association this week identified pound;26.4 million of slack within the draft budget for next year that could be directed towards front-line public services, including education.
The government's current budget plans will be put to the vote in the Senedd on Wednesday.