In Orlando, Jesse Ross sits at the switchboard of the Four C's day care referral service, fielding dozens of calls from parents seeking someone to look after their infant children.

In Wichita, the local referral service opened an infant care center this fall after it could not find a place to send children under 2. Within days, all 19 slots in the new center were filled, and a waiting list of 40 had formed.

And in San Francisco, the Child Care Switchboard turns away about half of the 250 callers each month seeking infant care, including one woman who offered to take her baby across town on four different buses to reach an infant care facility.

Only a couple of years ago, the idea of splitting very young children from their mothers and sending them to all-day infant care centers was considered taboo by most parents and all but a handful of child care experts.

But these days the demand for care facilities specializing in infants and toddlers under the age of 2 has exploded into the nation's fastest-growing child care need.

Fueling that demand have been several forces at work on the U.S. family. They include:

A rush into the work force of women who have children. Federal statistics show that while the number of children under age 6 has been dropping, the percentage of children under 6 with mothers in the labor force climbed from 28.5 percent in 1970 to 37.6 percent in 1977. By 1980, according to federal projections, that percentage will climb to 44.8.

A similar jump in the number of single parents. The increase has been caused by factors including soaring divorce rates and an increasing tendency among unmarried women who become pregnant to keep their babies.

Inflation rates that have made the once unusual two-income family a necessity in many parts of the nation.

Pressure on public and private facilities to provide more infant care has grown so rapidly that experts are still in the early stages of considering the merits and long-range effects on children.

"It's too late to argue," said Alice Honig, a Syracuse University child care specialist who is the aurthor of a recent book on setting up infant care facilities. "All we can do now," said Honig," is try to keep up."

But in the short run, at least, the need for infant care has far outstripped the availability of the somewhat specialized facilities needed for young children. In addition, experts note that the cost of such care is so high -- running as much as $75 a week -- that it could force parents to leave infants with the inexperienced or inept.

According to one estimate there are only a million day care openings in the United States for the six million children under the age of 6 who have working mothers.

"That means we really don't know who is taking care of those other kids," said Chicago child-care expert Bernice Weissbourd.

Infants and toddlers require more attention and a different type of stimulation than do older preschool youngsters, according to child care experts.

"Most states do not even require a license for someone to run an infant care facility with under six children," said Betty Caldwell, a University of Arkansas researcher who is one of the leading infant care proponents.

Still, smaller "family care" facilities are the type most parents with infants prefer, she said. Such facilities are often informal arrangements in private homes, which cost less than professionally staffed centers.

"You can get some place where the children just sit all day in front of a television set or scrawl at a coloring book," Caldwell said. "I've seen a lot of these places, and some of them are pretty discouraging."

Caldwell runs an infant care clinic in conjunction with the Little Rock public school system that is considered by some experts to be a model for early childhood care.

But Caldwell said that when she opened her first experimental infant care clinic in 1964 at Syracuse Univeristy, not a single state would agree to license an infant care facility.

"I was an outcast at the start, especially among the professional child care community," she said. "People tended to associate infant care with such things as orphanages. They thought the consequences of separating children from their mothers for a few hours a day would be very grave."

"Somewhere along the line," said Caldwell, "I stopped being an outcast and suddenly became a pioner."

One clue to that shift in attitude can be found in federal statistics on working women. In 1950, according to federal figures, only 9.5 percent of women with children under 3 worked. By 1977, that percentage climbed to about 35 percent.

Between 1970 and 1977 -- a period when women began entering the job market in droves -- the number of youngsters under 3 enrolled in day care programs climbed almost four times faster than the number of older preschool children, federal figures show. According to one study, the infant enrollment went up 11 percent in just one year, from 1977 to 1978.

Federal day care experts said the fastest growth in infant care has come in the South, with Texas and Florida the leading states. Overall, however, both federal and private experts said available openings for infant care have lagged for behind demand.

Officials at the Rosemont Center in the District of Columbia, which has 28 infants under full-time care five days a week, said they recently cut off their waiting list when it reached 400.

The center is located in a sprawling old building that onced housed a home for unwed mothers. Its infant clientele includes the children of docotrs, lawyers and politicians, as well as infants from less affluent families and single parents.

Rosemont officials said competition to get children into their center is so fierce that parents in some cases have resorted to the kind of string-pulling normally associated with getting young people into exclusive prep schools and colleges.

The center's infant program is run from several large, well-lighted rooms filled with toys and games. Each group of four toddlers and infants had an adult supervisor.

"If I hadn't been able to come here I wouldn't have been able to work, and I don't know what I would have done," Robin Pereira said last week during an interview, while her 18-month-old daughter, Anna, romped across the room with a large stuffed rabbit.

Pereira, an English teacher at American University, said she is a single parent who has been bringing her daughter to the infant care center since the child was three months old.

"She likes it, and I feel comfortable that she is learning an absolutely invaluable lesson in socializing with other children," Pereira said.

Rosemont Center's director, Louise Sullivan, said, "We don't try to be substitute parents for the children. We try to keep in close touch with the parents and to augment them, not replace them."