The budget agreement made this week by lawmakers to spend billions of borrowed dollars on building and refurbishing the city’s schools could push the state into the “milestone” debt range, experts said yesterday.

If the deal is approved by Governor Pataki, who is still reviewing it, it will provide the city with $11.2 billion over five years to build or lease 76 new schools, improve science facilities, and make improvements to existing buildings. The agreement, which Mayor Bloomberg has hailed as a victory, came just hours before the midnight deadline to print the bills on Tuesday.

Using what observers call a “backdoor” borrowing scheme – the bonds will never go before voters for ratification – the lawmakers hammered out a deal that gave the city $2 billion more in capital funds than was stipulated by courts to ensure the education of New York City children was up to par. In 1997, an education bond act was voted down by voters, which is likely to have pushed the lawmakers to find other ways to get it passed, the deputy research director of the Citizen’s Budget Commission, Elizabeth Lynam, said.

Of the $11.2 billion, $2.6 billion will be borrowed through the state Dormitory Authority, though the majority share of $1.8 billion will go only to the city. The other $9.4 billion is being borrowed through the New York City Transitional Finance Authority, and will be serviced equally by the city and the state.

“This moves us in the opposite direction of where the state needs to go,” Ms. Lynam said.”There is no doubt that the city schools need capital investment. However, the state should get its act together before passing out money it can ill afford.”

Ms. Lynam said the Dormitory Authority debt would “become the poster child for the need for constitutional debt reform in the state.” She said the new bonds could push the state into the $50 billion debt range.

Mr. Bloomberg, the Assembly speaker, Sheldon Silver, and the Senate majority leader, Joseph Bruno, hailed the decision this week as a necessary sacrifice for the education of the city’s children.

“This plan will mean dozens of new schools, tens of thousands of new classroom seats and a better education for our city’s children,”a spokesman for the mayor, Jordan Barowitz, said yesterday.

The governor’s director of the Division of the Budget said in a statement that the governor was concerned that the Legislature was putting forward a budget proposal with exorbitant $5 billion annual deficits for the next two years.

“Despite the governor’s ongoing concerns that the Legislature’s budget spends too much and reforms too little, we look forward to productive discussions with the Legislature over the next two weeks,” the director, John Cape, said.

The price of the agreement would be shouldered by the next governor, who would be stuck with the $500 million annual payments to service the debt and find it increasingly difficult to balance the state budget,a senior fellow at the Manhattan Institute, Nicole Gelinas, said.

“The problem is that the state will have to pay this debt for 30 years, though it’s a five-year project,” she said.”In another five years, the city will need more capital money.”

She added that the agreement would give the city too much money too fast.

“This gives the city an unprecedented amount of money all at once,” she said. “In the past, the city hasn’t budgeted its schools’ capital projects very well … You give the city the ability to start so many projects at once, it makes it difficult to oversee for fraud and abuse.”

Several observers said the agreement still avoided genuine reform of the education system.

The agreement makes no mention of increasing the number of charter schools allowed in the state, the spokesman for the New York Charter School Association, Peter Murphy, said.

“If you don’t have the accountability that charter schools bring, you are going to get the same poor results,” he said. “There’s nothing I can see in the budget that promises a change in the way the money is spent.”

It is against the law for the state to give charter schools any building aid, but Mr. Murphy said the agreement would undoubtedly benefit charter schools in “an indirect way.” Mayor Bloomberg and his schools chancellor, Joel Klein, have been helpful in getting charter schools space in the past, often by leasing them buildings owned by the city. If the city’s school buildings improved, the charter would likely be able to lease some of their buildings, he said.

A spokesman for Mr. Silver, Charles Carrier,said the lawmakers had decided to discuss the limit on charter schools after the budget is finalized and adopted.