As the Montgomery County school board performed its exacting, annual ritual of picking schools to build and repair, the question of what impression the inch-thick stack of requests would leave on the County Council was never far beneath the surface.

At a time when a flood of new students is straining schools' capacity, some board members said, they must convey a sense of urgency to the county government, on which the school system depends for money.

"I don't want to be in a position of providing space too little and in too little quantity," said board member Blair Ewing.

"If we think we need it now, let's . . . put the pressure on the financial authorities," another member, Bruce Goldensohn, agreed.

But through the two long evenings of deliberations just before Thanksgiving, board member James Cronin cautioned his colleagues again and again to practice moderation.

Each time other members suggested building or repairing a school more quickly than School Superintendent Harry Pitt had suggested, Cronin asked what project they would choose to postpone in exchange.

If the school board is trying to strike a delicate balance -- providing children with adequate places to learn, without appearing greedy -- it has good reason to be careful.

For one thing, it is asking for a lot of money.

Its $420 million "capital improvements" request -- a six-year program of construction for 19 new schools and other renovations for fiscal 1989 through 1994 -- is a sixfold increase over its request of five years ago. The amount of money the school system wants for next year alone -- $77.5 million -- is greater than the entire six-year program of 1984.

For another, this capital budget represents the first time the school system has asked the county government for money since spring, when a different kind of financial request -- the operating budget -- sparked the most fractious debate in recent memory between the county's two sets of elected officials.

In the end, school officials believe, the school system fared badly. Although the school system's budget was increased by 8 percent over last year's, the council nonetheless cut so deeply into the school system's request that the board was forced, for the first time ever, to pare services.

Since May, school and county officials have sought to mend their frayed relations. "We're talking more, and we're talking earlier," said the council's new president, Michael L. Subin, who also is chairman of its education committee. "The effort has been to get a much better understanding than we had last year."

The county government's reaction to this capital request -- starting next month, when County Executive Sidney Kramer gives the council his advice -- will provide the first tangible evidence of whether there has, in fact, been a rapprochement.

Traditionally, the school building and repairs projects funding, which accounts for about two-thirds of the county's capital budget, has been a less divisive issue than the operating budget. Unlike the operating budget, the capital projects do not create an immediate burden on taxpayers because they are financed primarily through the sale of long-term bonds.

County officials "have been very supportive, particularly with new school construction," said Philip H. Rohr, the school system's director of educational facilities planning and capital programming. Last year, the council gave the school system $326 million of the $376 million it had sought, including money to build seven new schools that are to open next fall.

Still, the county government now confronts a difficult choice.

With the school system asking to build 19 new schools during the next six years, can the county afford to pay for such an ambitious building program? But after the County Council pledged last year to allow houses to be built only in areas with adequate public services -- including schools -- can it afford not to?

Last week, Kramer, the county executive, was relatively noncommittal. He said he must balance the school projects against competing requests -- for roads, recreation facilities, child care centers, housing for elderly people, and the like -- some of which he has not yet reviewed.

"I can't tell you what the limit will be for schools," Kramer said. He added, however, "We will very carefully scrutinize all options other than building schools." They include changing school attendance boundaries, increasing the use of portable classrooms, and, perhaps, reopening schools that were shut during the 1970s as the school system's enrollment tumbled, he said.

In deciding how many projects to allow, he said, the county must be careful not to jeopardize its prized AAA bond rating.

Subin, the council president, said he believes the county is moving "dangerously close to the limit of what we can afford," without endangering the bond rating. He said the council may consider postponing some of the school renovations that the board has asked for. But, he added, Montgomery's unprecedented spurt in school enrollment does not give the council much latitude to trim the school board's request for new schools.

"We may not be able to put in an awful lot less," he said.