This is the year of the budget showdown in Prince George's County, and the opposing sides in the school debate faced each other last week when County Executive Lawrence J. Hogan held the first of two budget hearings.

On one side were the school supporters, defenders of the school system's request for a 9.1 percent increase in its budget. They are blaming the executive for the county's financial difficulties.

On the other side were Hogan's supporters, who say the county cannot afford this increase, especially as the county will have to contribute 19 percent more money to the school budget than it did last year because of state and federal spending cuts. Hogan's supporters blame school system waste for much of the budget shortfall.

And presiding over the debate was the Executive, as Hogan was described in the list of his achievements handed out at the hearing.

The budget hearings, which Hogan was attending against his will, are required by a 1980 charter amendment. Two years ago Hogan took out full-page ads in local newspapers in a failing attempt to urge defeat of the amendment.

He held the first hearing, last year, in a 49-seat room next to his office, leaving more than 300 school supporters fuming in the cafeteria listening over loudspeakers hooked up to the hearing room. Only about 60 citizens arrived this year, but security was tight. Visitors had to sign in. Maintenance men escorted them to the elevators and stepped aboard to push the buttons.

Only people who said they planned to speak were allowed into the hearing. Although the major topic of discussion was the school budget, the school system's official spokesman and public information officer Brian J. Porter was turned away at the door. "I was turned away last year, too," he said.

The Board of Education adjourned its own meeting and arrived en masse. And when the members took their seats, they found themselves facing an unsympathetic county executive and a big sign at the front of the room:

"Fiscal Year 1983 Budget Growth:

"Net revenue growth (Property tax at TRIM level): $15 million.

"(Percent increase: 4.2%).

"Requests for additional funds: Public schools: $34 million.

"(Percent increase: 19.3%).

"Comparable amount for all other agencies: $20 million.

"(Percent increase: 12.5%)

"Total: $54 million.

"SHORTFALL: $39 million."

"Shortfall" was written in red, and Hogan pointed to it as soon as the hearing began.

"The days when our citizens are willing to pay for government services without regard to cost are gone," he said. Anyway, "the issue is academic" because taxes cannot be raised in time to meet the fiscal 1983 budget.

Doris A. Eugene, school board chairwoman, was the first to speak. She and Hogan already had exchanged angry letters. Hogan blamed the schools for the financial bind the county is in. Eugene blamed Hogan.

Eugene defends the school system's budget request on the grounds that it is needed, and that school spending has grown less rapidly than the rate of inflation. She says the county should raise more money from the business community on which Hogan depends for support.

Hogan remained unfazed as she spoke. He poured himself a glass of water and chewed on his glasses. He leaned over to talk to Duncan, jotted down a few notes, and consulted Duncan again. Duncan leaned over and consulted Hogan's senior assistant, Edward L. Sealover.

By the time Eugene finished speaking, to the applause of the school supporters, the executive was ready to reply.

"I'd like to say for the record," he said, "that the school board's budget has gone up in the last three years 32.3 percent, while the overall county budget has gone up 4.5 percent." And the county has spent only $350,000 for economic development, he added. "So I think that should be kept in perspective."

As soon as the second school board member, Bonnie F. Johns, had had her say, William J. Goodman and fellow TRIM committee member Col. John T. Gleason leaped to Hogan's support. Goodman is one of the men who wrote the TRIM amendment.

Gleason praised Hogan for his "courage and determination" in eliminating wasteful spending and presented him with a plaque.

Then Goodman lashed out at school spending. Among other money-saving techniques, Goodman recommended closing junior highs and middle schools and ending school bus service in urban areas. "We have an uncontrolled system of public education that caters to a few privileged children whose parents generally are the leadership of the PTAs," Goodman declared.

This brought laughter from the school types. Melanie Goldsmith, the student member of the school board, shook her head and wrinkled her brow. "I wasn't sure what he was saying," Goldsmith said after the hearing. "But it didn't sound true."

Another school system critic, Roy L. Chambers, noted that the school budget had grown by 14 times since 1964, while the county budget had grown by 12 times. But he blamed most of the financial difficulties on "cross-county busing."

This sort of talk was enough to stir the ire of English teacher Sarah McKinney-Ludd, who complained of overcrowded classrooms and inadequate funding. "Rubber bands and paper clips are now given in envelopes of five," she said.

And it was enough to anger Joanne Benson, who represented the Willing Workers of Hill Road, a small community group in the Seat Pleasant area. She noted that Montgomery spends 28 percent more for every pupil than Prince George's, and that the District spends 20 percent more.

Inadequate spending on education caused serious community problems, she said. She had already noted an alarming resurgence of racism, she said, adding that unless something was done there was the "possibility of rioting in the streets" and "other problems too numerous to name at this time."

"For the record," said Hogan when she finished, "I think we ought to talk about wealth discrepancy." One penny of property tax assessment yields $1,010,000 in Montgomery County, Hogan said, but only $660,000 in Prince George's. The "piggyback" income tax will give Montgomery $149.5 million this year, but only $102.6 million to Prince George's. He did not mention the District.

And so it went on, full of sound and fury, signifying . . .

"I don't know if he heard us, but it keeps some of us from having ulcers," said Eugene.

"I don't know that it made any difference," said Goodman.

Said Hogan: "The buck stops here. That's the problem."