Prince William County politicians smile ruefully when they tell the story of the promising young man who was recruited recently to be a county police officer.

The rookie entered the Northern Virginia Criminal Justice Academy as a Prince William recruit but emerged as a Fairfax County police officer. The enticement: a starting salary in Fairfax that was $4,000 higher than that in Prince William.

It was not the first time the fast-growing jurisdiction on the western fringe of the Washington suburbs had lost out to one of its richer neighbors -- and officials say it probably will not be the last.

A combination of factors in Prince William is causing county officials to face tougher choices than ever before to provide services for a burgeoning population, county officials say. The county is struggling to compete with its neighbors for personnel at the same time it grapples with growth that has strained to the limit the county budget for facilities and services.

"We have got to be more competitive," said G. Richard Pfitzner, the newly installed Democratic chairman of the county Board of Supervisors.

"We [must] think bigger, plan larger and for longer term," County Executive Robert S. Noe Jr. told the board last month. "Our change is exponential."

The expanding needs of Prince William, whose population of about 170,000 is expected to grow by 5,000 annually through the turn of the century, are forcing local politicians to make tough -- and politically risky -- choices in a county where bond referendums are frequently defeated.

The most pressing needs cited by county staff members include:

* Higher teacher salaries. School administrators are asking for $6 million to raise salaries. The money would boost the starting pay of a teacher with a bachelor's degree to $16,000 from $14,280 annually.

* Higher salaries for county employes, who have not had a raise above cost-of-living adjustments since 1980.

Increased staff for county development offices.

* Libraries. The county has only two public libraries, one of which is extremely crowded. Mini-libraries -- storefront operations that will lend paperbacks -- are scheduled to open over the next several years, but are considered a stop-gap measure until a full-service library is built.

* A recreation center, including an indoor swimming pool. County officials say that the county's high school swimming teams now must go to Fairfax to practice -- often before 6 a.m. There is only one indoor swimming pool for general use in the county.

In addition, county officials say drainage improvements, renovations to run-down county office buildings and a communications center for county police and fire services are pressing needs.

"A lot of these things are taken for granted in places like Fairfax," said one county official who asked not to be identified. "But we're just now reaching a level [of population] where we can no longer get by without these facilities. The demand is just too great."

County staffers say the competing demands for money put an unprecedented strain on resources. "We expected A, but we got A plus one," said Director of Finance Connie Bawcum. "We didn't anticipate the magnitude of the [demands]."

County executive Noe, who is scheduled to submit his budget to the board March 5, hints that he plans sharp increases in the number of county government employes, as well as steep pay increases for them.

Some supervisors think there is not much political support in fiscally conservative Prince William for bigger government and better paid government workers. "There is no constituency for custodians," said board chairman Pfitzner.

Yet despite what county officials consider great demand for new facilities, Prince William voters have defeated nine of 11 bond proposals in the past decade.

As a result, the board stepped in and used regular budget funds to pay for facilities, such as a new jail and expanded library services, that voters had rejected. A budget surplus that stood at $11.8 million in 1981 was used to pay for a variety of construction projects, including the first phase of a new government headquarters on Davis Ford Road.

"If the next referendum is not successful," said Supervisor Kathleen K. Seefeldt, "we are not going to have the resources to step in and fund those new projects." The next referendum, scheduled for 1986, would fund a new regional library, a police-fire rescue training center and park improvements.

Supervisors say it is unlikely they will raise the real estate tax, now set at $1.42 per $100 of assessed value. Each penny on the tax rate means $500,000 in county income. But even if a penny or two were added to the rate, officials say, it would not make a dent in the county's capital needs.

And while a number of big businesses recently have opened or have begun construction -- including one of the largest discount malls on the East Coast -- and they are expected to produce large amounts of new revenue for Prince William in the long term, the short-term choices still are painful, officials say.

"You're fighting a holding action," said Supervisor Donald E. Kidwell. "You just try to keep from being overwhelmed."