When research psychologist Steven Barry moved to Arlington from Chicago 2 1/2 years ago, he discovered a network of community services tailor-made for young, two-income families just like his.

When the time came to find day care for his young son Benjamin, Barry was referred by the county's Child Care Office to 14 different child care centers, each of them inspected and supervised to conform to county standards.

To Barry, these references were crucial. Although he visited all 14 centers personally before settling on the Clarendon center, he felt better knowing that his choice had first been cleared by professionals asking questions he might never have dreamed of.

"Arlington attracts young professional families because of its direct services," he said, "That's what makes it different."

Now, thanks to federal budget cuts, Arlington's Child Care Office is in danger of losing its clout. As of Oct. 1, the office's funding dropped from $168,000 to $75,900, which would mean no more inspections, no more annual directories of available day care, no more training workshops, no more follow-ups on complaints and a halt to the county's yearly immunization survey

Alarmed by the cut in services, Barry last week made the transition from silent citizen to community activist. On Saturday, he and a handful of other parents surfaced before the Arlington County Board as a new and militant constituency brought together by the unexpected impact of the federal government's budget-cutting on their own lives.

"I hadn't expected to see things initiated on the national level not only hitting my pocket book, but affecting my children," said Jeffrey Kaye, a 30-year-old entrepreneur with a 4-year-old son enrolled in the Sugar Plum Nursery, "Now that it's affecting me in my backyard, I'm not too sure about Reagan's budget and economic concepts at all.

"There are some things you just don't cut back on," said Kaye,"I believe that a community's fundamental interest lies in child care, in keeping its children healthy and educated."

For the Arlington County Board, the child care lobby was another in a string of interest groups that have coalesced in the wake of the Reagan budget cuts. For the board, the dilemma lies in dividing up $1 million in county contigency funds, set aside in anticipation of the federal cuts, among about 30 local programs that together have lost $3.1 million in federal funds.

Last month, the board doled out $279,000 for a series of high-priority programs, including a counseling program for Indochinese refugees, direct day care for adults and children, and homemaker services for the elderly. With approximately $500,000 tentatively earmarked for cuts expected in school funding, the board now is left with only about $220,000 to be spread among various clamoring groups.

Board members Ellen Bozman and John Milliken, both Democrats, last week emerged as the champions of the Child Care Office. "In this community, we've been supportive of day care since 1943. These are the kinds of things people really want to keep," said Bozman, citing a recent national study of demands on local government services, "And that's been the attitude in Arlington."

But Dr. Martin Wasserman, the director of the county Human Resources Department who now is facing both local and federal budget cuts next year, had to admit that in combing through county needs, the Child Care Office did not emerge as a high priority. "They are on the margin compared to much more important core services," he conceded.

For board member Dorothy Grotos, the cheers and boos from the audience of parents could not outweigh the needs of groups -- including those likely to be included in the next round of federal budget cuts -- not yet heard from.

"Every special interest group has its fans out there," she said, "There are some clients who are going to need these dollars a lot more than the clients before us today . . . If we continue to do this, we will use up our resources by the very beginning of the process."

For the board on Saturday, the answer to the dilemma was a compromise. The Child Care Office was given $19,000 -- down from its request for $34,000 -- to allow continued inspections of day care centers, but not of the 265 homes in the county that provide day care to small groups of young children. Day care for low-income families will continue to be monitored.

For Kaye the battle is not over. He is not concerned that the quality of care at the Sugar Plum Nursery, where his son Ryan is enrolled, will drop but, he said "I have to think of other people." With that goal in mind, Kaye is going to look for help outside government to maintain what is to him "an essential service."