They claim that the figure of Pounds 548 million - out of a total budget of Pounds 733m - is based on a guess about how much money councils are already spending on the under-fives.
And they say that the Pounds 165m of "new money" intended to provide vouchers for the 150,000 or so four-year-olds not currently in state education may not be enough.
The calculation of the number of children not in state nurseries is based on information from the Office of Population Censuses and Surveys. But, according to the Association of Metropolitan Authorities, "the OPCS attaches a high degree of uncertainty to its estimate of the total four-year-old population".
And it warned: "If the figure proves to be a serious underestimate then either the total amount of money available will need to be increased, or the value of individual vouchers will have to be reduced."
It said the amount of money to be made available for vouchers, due to be piloted from February, was still imprecise.
The Government plans to recycle Pounds 548m that it says authorities currently spend on under-fives via vouchers for parents. The "new money" will go directly to the voucher-issuing company.
Money will be distributed to authorities through the under-fives SSA (standard spending assessment) and then clawed back for every four-year-old in state education.
Local authorities are given pre-school and primary SSAs by the Department of Environment. However, they do not have to spend according to these SSAs - they could spend less on the under-fives and more on primary, for example. They are also not required to distinguish between their primary and pre-school spending in the SSA returns they make to the Government.
The Department for Education and Employment has, in fact, always insisted that councils were not able to do this calculation. Now, however, in taking Pounds 548m from the current national under-fives SSA which totals Pounds 963m, the DFEE appears to have decided what the LEAs spend on the under-fives.
Analysis by both the AMA and the Association of County Councils suggests that the proposed scheme will penalise authorities like Solihull with good nursery services as a large part of their SSA will be clawed back.
Authorities with few or no services for their under-fives will lose only a small part of their SSA.
The AMA believes that "there is, therefore, no incentive for them to expand provision but every incentive for them to continue to divert the money received via this SSA into other service areas."
Ministers plan to use data on the number of four-year-olds in school on census day next January to fix the amount that will be clawed back from local authorities in 1997 and subsequent years.
It will not be updated, unlike the population data used in the SSA formula which is revised annually. This could lead to authorities with falling rolls receiving less money than they spend.
"In discussion with the DFEE it was immediately apparent that they had not spent much time on devising the methodology and had given no consideration at all to the considerable problems its implementation would cause," said the AMA.
It appears that the child benefit database may be used either to send out the vouchers, or more probably an application form for them, but the DFEE has yet to clarify how often vouchers will be issued and for what period of time - yearly, termly, half-termly.
It is also unclear what will happen to the money if parents decide to transfer a child to another school in the middle of a term.