As many as 400 people a day pack the counter at the Fairfax County Traffic Court to pay fines. Dozens more sit out their cases in courtrooms down the hall as judges wade through overloaded dockets. Traffic court clerks say their phone lines are jammed constantly.

"We can't handle the telephone calls, we can't spend the time with people at the counter," says General District Court Clerk Catherine Ratiner. "People sit in court longer and have to wait longer to be taken care of."

Such laments are heard increasingly from officials throughout the Washington area, because traffic court cases and traffic arrests have skyrocketed in recent years and particularly in recent months. Hit especially hard are Fairfax County and other Northern Virginia jurisdictions, which are just now feeling the backlash from new laws stiffening penalties for traffic violations and increased police enforcement of traffic laws.

Maryland's traffic caseload also has risen dramatically since tougher traffic laws became effective in recent years, and in the District officials expect arrests resulting from harsher drunk-driving laws enacted in recent months to begin squeezing city courts soon.

A survey of local courts showed:

* In Fairfax County, new traffic court cases were up 15.6 percent in the first nine months of 1982 compared with the same period last year. "Last January we could schedule two courtrooms a day with one commonwealth's attorney handling all the cases," said Assistant Commonwealth's Attorney Jack Robbins. "Now we have three courtrooms going regularly and a commonwealth's attorney in each court."

* Arlington General District Court officials estimate traffic cases have increased from last year's daily average of 125-150 cases to about 200. "Our phone lines ring constantly from 8 a.m. to 5 p.m.," said Arlington Deputy Clerk Kathleen D. Sheehan. "One man told us he'd been trying to get through for days."

* Prince George's County traffic court cases have escalated 31 percent in the past five years, said Michael O'Ferrall, administrative clerk of the district court.

Some of the increase is attributed to police writing more tickets. In the first 10 months of 1982, for instance, Fairfax County police made 37 percent more traffic arrests on charges of speeding, drunk driving and other offenses than during the same period last year. At the same time, Virginia State Police increased traffic arrests by 31 percent on Shirley Highway and the Capital Beltway alone. And Maryland State Police issued 28 percent more traffic tickets on Prince George's and Montgomery highways over last year's figures.

Some police departments are increasing patrols, while others are strengthening their techniques for nabbing drivers breaking the law. Fairfax County police have added 60 officers to the department this year, while Virginia State Police have assigned 16 new troopers to patrol the Shirley Highway/Capital Beltway areas, police spokesmen said.

Montgomery County police late last year began using roadblocks to catch drunk drivers and other traffic law violators, and Maryland state troopers have been targeting accident-prone stretches of highways for more patrols, police said.

Under pressure from local and state lawmakers and grassroots citizens groups, police have stepped up drunk-driving law enforcement. "Ten years ago you could barely get a conviction in a drunk-driving case," said Walter Shoup of the Arlington Police Department records division. "Now there's a change in the public attitude and we're making more arrests."

Despite the increases, court officials say they haven't seen the deluge of cases expected from the spate of new drunk-driving legislation. Although drunk-driving arrests by Montgomery police have more than doubled this year and are up substantially in almost every area jurisdiction, drunk-driving court cases are barely up, officials said.

"Everyone thought the results would be much more consequential," said Marvin H. Wagner, a local attorney and chairman of the Fairfax County Task Force on Drunk Driving. "We figured everyone would go to trial to contest their tickets, but there's been virtually no increase in trials."

Fairfax Traffic Court Clerk Ratiner said Virginia's new drunk-driving law enacted July 1 is too new to have generated more court cases. But, she said, new regulations have dramatically increased paper work for court staffs, which are now required to conduct lengthy interviews of most individuals convicted on drunk driving charges.

And while Virginia lawmakers gave judges tougher orders to suspend licenses for drivers convicted under the laws, they also created a new category of driver's licenses to accommodate those offenders. Drivers convicted under the law are eligible for special restricted permits that may be used for driving to a job, school or church--all more work for the court staffs, Ratiner said.

Other changes in laws for processing traffic cases have had just as great an impact on courts, officials said. "We're backed up as much as 1 1/2 years on sending some conviction records to the State Department of Motor Vehicles," said Arlington's Sheehan.