Fairfax County's top elected official, upset with the traffic-choked roadways that lead to the county's government and judicial headquarters, is putting the pressure on Fairfax City to come up with a solution.

In a recent session with The Washington Post, Fairfax Board of Supervisors Chairman John F. Herrity said it is vital for the county's north-south traffic that congestion on Chain Bridge Road be eliminated. In a separate interview last week, Herrity said that the county government would consider moving its headquarters west to the 183-acre site it owns across from Fair Oaks Mall if the city does not improve its overwhelmed roads.

"I suggest the city officials go ahead and do their duty . . . in terms of [solving] its [the city's] transportation problem," said Herrity. "You have to be a babbling idiot not to figure out that you need to widen [Rte. 123]."

"Moving the government center from the city has been discussed many times," said Fairfax City Mayor George T. Snyder. "I don't know if it's a promise or a threat."

During peak rush hours, motorists frequently spend 30 minutes driving the two miles of Chain Bridge Road (Rte. 123) that extend from the I-66 interchange to the southern city limits near George Mason University. Herrity said Fairfax City's roads could possibly have adverse effects on ridership of the Vienna Metro station, scheduled to open in the spring of 1986.

But Snyder is moving cautiously despite Herrity's ire. Snyder said the city's transportation task force would soon study a recently released traffic and transportation report that offers ways to untangle the suburb's roadways.

"It's true that certain improvements have to be made to Rte. 123, and this council will make them," Snyder said. "The recommendations can't be implemented overnight; anyway, it will take four or five years to upgrade the roads as it is."

The $26,600 traffic study, done by JHK & Associates, a private Alexandria-based consulting firm that specializes in transportation, warned of worsening gridlock and bottleneck situations at the city's major intersections. It also forecast even longer delays in getting from one end of the small community to the other.

The report gave its highest priority to widening the two-mile stretch of Rte. 123 to four lanes all the way to the southern city limits. To date, the city has widened the busy road only near county offices in the Massey Building and around the I-66 interchange.

"Traffic in the city will never be better than it is today," said Jeff Lindley, author of the 80-page report. "The situation now along Rte. 123 is intolerable . . . and until conditions are improved it will only get worse."

But Fairfax City, with a population of 20,500, is in no hurry to upgrade the heavily traveled two-lane road, with historical roots dating to the 1800s, just to accommodate commuters and to appease county officials. Indeed, many residents believe the City Council's attempt to widen the road 11 years ago resulted in political suicide for a majority of its incumbents.

Council member Glenn L. White, who lost his 1974 re-election bid after supporting the widening of Rte. 123, said he feared "another revolution" if the council voted "to support something that will destroy the character of the city."

The report also recommends straightening a scenic, tree-lined bend in Rte. 123 called Rust Curve that passes around an affluent town house development. After eliminating the curve, consultants said the city should install a guardrail or bumper to "prevent cars from hitting the large trees on the east and west sides of the roadway."

While council members admit the city's road network is overburdened and needs some sort of upgrading, most are hesitant to support any changes to Rust Curve. "If we straighten out Rust Curve and destroy the trees there, we'll wind up with a sterile, concrete atmosphere and environment that prevails in other jurisdictions that aren't quite as attractive as ours," said White.

Herrity said the county is working on plans to ultimately widen and extend Shirley Gate Road to Rte. 50, which would bypass Fairfax City and give commuters from the south and west an alternative to Rte. 123 and Main Street. The consultant's report said the Shirley Gate Road extension would "shift at least 6,000 vehicles per day onto the bypass from city roadways by the year 2000."

"If the city widens Rte. 123, [the county] would bypass Shirley Gate around the city," said Herrity.

"That's a common comment I've heard from [Herrity] in the two years I've known him," snapped Snyder. "If the county wants to come in and speed up the process as a result, I have an open hand."

The Shirley Gate Road extension was first included in the county's comprehensive plan in 1975 and has been in the design stage since August 1984. A spokesman in the county's planning and design division said his office hopes the construction will be included in the proposed road referendum this fall.

The traffic report's other recommendations include widening Jermantown Road to five lanes between Rtes. 29 and 50; upgrading two-lane Roberts Road between Main Street and the southern city limits, and widening Old Lee Highway to three lanes between Layton Hall Drive and Army/Navy Country Club Drive.