A clash over education spending is heating up between the state’s Democratic governor and the Democratic speaker of the Assembly.

As the administration wrestles with the final details of its 2008-09 executive budget proposal, which Governor Spitzer is slated to deliver to lawmakers in three weeks, the governor is waging a delicate balancing act: between his fiscal and political priorities. Nowhere is the terrain trickier than on the issue of public school aid.

Speaker Sheldon Silver, a stalwart ally of the city’s teachers union, is letting it be known that he expects Mr. Spitzer to stay true to his pledge to set aside more than $1 billion in additional school aid in this year’s budget.

Keeping his promise even while crafting a balanced budget may be a luxury the governor and the state cannot afford.

The state’s deficit under Mr. Spitzer has soared to $4.3 billion — a figure that some fiscal observers predict could grow to $6 billion, or even $8 billion, due to the slowdown in the financial services sector.

The administration is strongly considering scaling back Mr. Spitzer’s ambitious four-year plan to increase school aid by $7.6 billion, according to a source familiar with budget office discussions.

Mr. Spitzer has said he would pump an additional $1.4 billion into the education system during the next school year. That figure may be significantly reduced, the source said.

Despite the shaky economy, which could result in lower-than-expected revenue for the state government, Mr. Silver is warning the governor not to renege on his promises. “I do not want to see a deviation from it as a result of an economic downturn,” Mr. Silver told The New York Sun last week.

The disagreement over spending priorities threatens to jeopardize the cooperative relationship that Mr. Spitzer has developed with Mr. Silver, who has risen to the governor’s defense as Senate Republicans — and even members of the speaker’s Assembly conference — have turned their backs on Mr. Spitzer.

A spokeswoman for the governor, Christine Anderson, said the administration would like to preserve its original spending forecasts, but isn’t making any guarantees. “There is a serious sense of not wanting to back away from any of it,” she said.

Mr. Spitzer is already preparing to slash Medicaid funds to hospitals and nursing homes, and to announce a hiring freeze on many state government jobs considered nonessential, according to a source.

The next few weeks could also test Mr. Spitzer’s relationship with education funding advocates, who have stood out as of one the embattled governor’s staunchest supporters.

By tabling his long-term spending plan, Mr. Spitzer risks rekindling the legal battle over public school aid that education groups waged against the Pataki administration.

“It’s our intention to work with the governor to fulfill that commitment,” the executive director of the Campaign for Fiscal Equity, Geri Palast, said.

“At the end of the day, these kids have waited 14 years. If you’re going to reshape the budget in any way, this is not place where you should look,” she said.

The nonprofit corporation, composed of a coalition of parent groups, school boards, and other advocacy groups, sued New York in 1993, claiming that the state shortchanged New York City public schools and other urban school districts. In 2006, the Court of Appeals ruled that Albany must increase state aid to New York City public schools by at least $1.93 billion over a multiyear period.

When he took office, Mr. Spitzer vowed to satisfy the legal complaint of the group — even going beyond what state courts required — through a four-year plan of spending increases.

His plan calls for raising total education aid on a school-year basis by $7.6 billion over the course of his term.

About 70% of that total — or $5.5 billion — would be distributed as “foundation formula” aid, which is steered primarily to poorer school districts. The governor’s office said the New York City school system would see an increase of $3.2 billion in aid over four years.

This year, the state adopted the first piece of the plan, passing a budget that increased education aid over a school-year basis by $1.8 billion, $1.1 billion of which consisted of “foundation” money.

The governor’s office has promised a further increase of $1.4 billion for the second-year installment, including $1.25 billion of “foundation” money.

Public school aid is just one area in which Mr. Spitzer has pledged big dollars. He has said he would implement a number of the recommendations made by a state-appointed higher education commission, which advised spending hundreds of millions of more dollars on the state’s public universities.

The governor also said he would hold firm on his promise to increase spending on a property tax relief program by another $400 million this year.

Fiscal observers say that given the size of the deficit, Mr. Spitzer has put himself in a bind.

“If there is not any deviation, the budget hole will not be closed,” a budget analyst for the Manhattan Institute, E.J. McMahon, said. “This is why governors have not been in the habit of promising large, multiyear school aid increases. He really stuck his neck out with this.”