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TRENTON IN AN effort to get a handle on the growing problem of trying to find some way to balance his first state budget, Governor Kean is preparing to create an Office of Management and Budget similar to the one run for President Reagan by David T. Stockman.

Since it embodies his philosophy and emphasizes those programs he deems worthwhile, the budget is the Governor's political document. However, Mr. Kean is having a difficult time finding enough money to keep the basic machinery of the state's government running efficiently, much less institute any new programs designed to effect the types of changes he believes in.

Current estimates of the shortfall that the Governor faces range up to $400 million. This is a considerable sum, especially in light of his pledge not to raise taxes and of the sudden cutbacks in Federal largesse.

Mr. Kean originally was scheduled to deliver his budget message to the state's lawmakers on Feb. 15. However, this was moved back to March 15 by the Democratic-controlled Legislature to give the new Republican administration more time to find those economies in government that everybody talks about during campaigns.

Last week, the Democrats offered to delay the budget message deadline by another month. But this seemingly generous offer by State Senator Laurence S. Weiss, Democrat of Perth Amboy, and Assemblyman Robert C. Janiszewski, Democrat of Jersey City, chairman and vice chairman of the Joint Appropriations Committee, was designed to increase, not diminish, the political pressure on Mr. Kean.

The two lawmakers said they wanted the new Governor to have all the time he needed to get the job done, and added: ''This is Tom Kean's budget, not Brendan Byrne's.'' In other words, the Democrats wanted to foreclose the time-honored apologia allowed all new Governors -that their first budget is really a hand-me-down from the prior administration and one over which they have little control.

And the Democrats further disclosed their real motives by including a partial transcript of the remarks Mr. Kean made during a campaign debate with the Democratic candidate for Governor, Representative James J. Florio of Runnemede.

In the transcript, Mr. Kean was asked how he would cope with a large deficit, given his promise to cut business taxes and, if possible, the state sales tax.

''I really don't think that in a $6 billion budget I'm going to have that much trouble finding the money,'' Mr. Kean said. At the time, he was talking of a $100 million shortfall. Actually, the last Byrne budget, which ends June 30, is expected to have a $100 million surplus.

The budget-balancing problems have been created, at least in part, by Governor Kean's promises and President Reagan's projected Federalaid cutbacks and shifts of responsibility.

Mr. Kean has said that he would not drop minimum school aid for affluent districts, something Mr. Byrne did to balance his last budget. This $65 million item was restored by the Legislature for political reasons in an election year and, although the sum is not large, it becomes part of a larger problem.

The Byrne administration also used $83 million in gambling-casino revenue funds to finance exisitng programs for the elderly, thereby relieving that amount of pressure on the general state budget. Again, Mr. Kean said that he would not do that again, and that adds $83 million to the problem.

President Reagan, in addition to proposing a $700 million reduction in Federal aid to New Jersey next year, also wants to take back some $40 million in funds promised for the current year.

Add that to the list of growing problems - along with state employees' salary increases and the usual litany of items affected by inflation (which means almost everything but state tax revenue) - and the size of the task begins to become apparent.

It is impossible to get anyone in the Kean administration to talk about hard figures. There is a lid on any mention of money and programs, and since preoccupation with the budget is consuming everyone's attention, there is very little visible activity around the State House these days.

Mr. Kean's choice to play the David Stockman role in his special budget office is Alfred F. Fasola Jr., who helped run his successful recount of the votes cast in the Nov. 3 general election and was a member of his transition team.

It will be Mr. Fasola's task to examine the budget - department by department and line by line - to look for the fat everyone says is there, and to pump some long-range economies into the system, which is going to be on short rations for a long time to come.
POLITICS - KEAN, FACING BUDGET PROBLEM, MAY APPOINT A 'STOCKMAN' - NYTimes.com