ALBANY — Assembly Democrats today are proposing up to $2 billion in borrowing to help close the state’s $9.2 billion budget deficit, while also restoring about $600 million in cuts to public schools that Gov. David A. Paterson said were necessary to stabilize the state’s finances.

Assembly Speaker Sheldon Silver, D-Manhattan, said the borrowing would help pay state operating costs—a move derided by fiscal watchdogs as irresponsible. The Assembly plan calls for about $800 million in school aid cuts, compared with the $1.4 billion proposed by Paterson.

“We’ve always stood for education,” Silver said.

Silver’s defense of funding for schools came as three of his fellow Democrats called on a politically potent teachers union to support a pay freeze for teachers across the state as a way to avoid mass layoffs and cuts to programs.

The Assembly’s budget proposal, like the State Senate’s, also would reject Paterson’s plans to permit wine sales in grocery stores and impose a new tax on sugar-flavored beverages, such as sodas. The Assembly, though, was expected to embrace a $1-per-pack increase in the cigarette tax.

Release of the Assembly plan is likely to do little to ensure an on-time budget before the 2010-11 fiscal year begins April 1. Lawmakers are to leave here Friday for an 11-day break for religious holidays.

The Assembly plan, Silver said, includes a proposal by Lt. Gov. Richard Ravitch to borrow up to $2 billion in the coming year — a move that would let the state solve about 22 percent of its deficit through the use of floating bonds.

Three members of the Assembly’s Democratic Conference said Tuesday that “teachers must be a part of the solution” to help close the deficit and prevent layoffs and larger class sizes.

In a letter to the head of the New York State United Teachers, the Democratic lawmakers — Assemblymen Sam Hoyt of Buffalo and Michael Benjamin of the Bronx and Assemblywoman Ginny Fields of Suffolk County — said a statewide freeze in teacher pay would save more than $1 billion and help prevent teacher layoffs.

Hoyt said that more Democrats have expressed a possible interest in signing on to the proposal outlined in the letter.

Richard C. Iannuzzi, the NYSUT president, said the letter fails to recognize dollar savings already driven by teachers during the recession. He said that 5,000 teachers have been laid off in the last year and that a number of local NYSUT unions reopened contracts and agreed to either no pay increase or a raise of 1 percent.

The NYSUT leader said lawmakers also need to look at raising taxes on the wealthy. “What I see is a message that says working people need to sacrifice and those who have been successful during this difficult economy do not,” he said. “. . . I don’t see . . . shared sacrifice.”

Iannuzzi said the $800 million in school cuts, along with ideas to help districts save money and tap into reserve funds, is “a number we can work from.” He said lawmakers should be quickly passing an incentive plan for early retirement to encourage higher-paid, older teachers to leave the payroll.

Hoyt, Benjamin and Fields said that teacher salaries are the top expenditure for districts and that the base and the step increase for teachers last year outside New York City rose by an average of 5.6 percent at a time when private-sector wages were dropping.