Fairfax County officials, who have talked eagerly of getting the help of private developers to begin construction of a new county governmental complex, are conceding that chances of building such a project appear to be sharply limited by Virginia law and by the sheer complexity of the undertaking.

Nonetheless, the idea seems to have gathered its own momentum, and longtime champions and critics of building a new government center have endorsed exploring how the county might get the project started with the help of a private investor and at little cost to the taxpayers.

"As far as I'm concerned, we can build a circus tent and put the bureaucrats in it," said County Board Chairman John F. Herrity, a Republican who seldom lets slip a chance to bash the proposed complex.

But Herrity has become one of the main advocates of examining a joint venture on a county-owned tract west of Fairfax City.

The Board of Supervisors has twice decided not to put the complex on a ballot for approval by voters, and conventional political wisdom in the county is that voters are not eager to approve what some supervisors have called "a monument to bureaucracy."

Nonetheless, most county politicians acknowledge that the county, which spends about $5 million a year leasing office space, needs a larger government headquarters.

Michael S. Horwatt, a lawyer who chaired the first relocation study in 1978 and still supports such a move, called a joint venture "an avenue for the county to have its cake and eat it too."

The site for the proposed complex is a 183-acre tract of prime real estate near Fair Oaks Mall at I-66 and Rte. 50. No construction has ever taken place on the land, which is thought to be worth at least $40 milion and $60 million, depending on how it could be used.

Fairfax bought the land in 1982, with the government center in mind, when it became apparent that the county had outgrown the 12-story Massey Building in Fairfax City, the now-14-year-old county government headquarters. A proposed building at the Fair Oaks site would almost double the floor space of the Massey Building.

County staff members are in the preliminary stages of drawing a proposal for developers to submit bids for a joint venture. But even among the most enthusiastic supporters of the plan, doubts remain.

For example, county officials said, one of the best ways to set up a joint venture would be for the county to sell the building to investors who would lease it back to the county and receive huge tax advantages from the depreciation of the facility. However, such a deal is improbable because state law, although not explicit on the issue, appears to bar localities from signing long-term leases that obligate future local governments.

Another option for a joint venture is a so-called turnkey project, in which a developer would construct a government center and then hand it over to the county, which would need only turn an imaginary key at the front door and take possession. In return, the county would give some portion of the 183-acre site to the developer.

Herrity said he supports a turnkey plan, which he likens to a recent deal in which the county donated 26 acres of land near Reston to the Fairfax Hospital Association, which agreed to build a $10 million center there.

County Executive J. Hamilton Lambert said, however, that turnkey deals are better suited to smaller projects than the government center, which is expected to cost more than $70 million to build.

"There is a narrow financial window available to the county," he said.

Deputy County Executive Denton U. Kent warned: "A developer will be coming in here with a deal leaving us the least amount of land for the government center and taking the most land for himself with the highest building density possible."

Although Fairfax officials say they have already received eight or nine inquiries from investors interested in a venture with the county, some developers said the task of putting together a viable deal is daunting.