City public schools are likely to face program cuts next year under the new budget proposed by Mayor Bloomberg yesterday, though pressure from a coalition including the principals union, the teachers union, and the Campaign for Fiscal Equity could lighten the blow.

The coalition Friday will kick off a full-scale campaign complete with radio, television, and print advertising to make the case that the mayor’s budget reneges on a promised $450 million increase to public education.

The message challenges a claim Mr. Bloomberg made yesterday in releasing his budget: that he has actually increased funding to public schools by more than $200 million. School officials said the increase, $234 million to be precise, comes in part from added expenses to cover new needs the Department of Education has estimated, and in part from Mr. Bloomberg’s decision to insulate the department from a 3% budget cut ordered in March, cuts some other agencies are facing next year.

Yet the net amount the public schools are gaining, by Mr. Bloomberg’s tally, does not account for losses the education department faced during this fiscal year and projected losses already tabulated into next year’s budget.

The Department of Education faced $180 million in midyear budget cuts this year, leading the city to shave an average of $70,000 off each school’s budget.

Then, predicting an even more dismal economic outlook for fiscal year 2009, City Hall projected two additional losses, first of more than $300 million and then of $215 million. Only $111 million of those cuts have been restored.

Comparing the budget first implemented last year to this executive budget, the Department of Education’s net change is a modest gain of about $56 million.

Considering that the cost of many programs grows larger every year — teacher salaries, slated to see a 5% raise this month, are a prime example — that increase will probably not be enough to spare the public schools from having to cut some programs and services.

Indeed, part of the $234 million increase Mr. Bloomberg touted stems from what the department calls “new needs,” such as an extra $22.6 million for breakfast and lunch due to rising food prices, and an extra $70.2 million to pay tuition for public charter schools, which are expanding substantially next year.

Speaking to reporters yesterday, Chancellor Joel Klein said he expects more than $300 million in program cuts.

“I hope that a significant portion of that can be taken centrally, and that is what I’ve been working on,” he said. “But some portion will be distributed to the schools.”

The advocates campaigning for more funding said they aim to repeat their recent success in lobbying Albany to hand the city schools more than $600 million in new funds, despite an early budget by the former governor, Eliot Spitzer, that allocated a much smaller increase.

“The mayor rightly understood it was important to keep his $400 promise to homeowners,” the UFT president, Randi Weingarten, said. “He should have given the same consideration to the importance of the four-year promise the city made to our children.”