To students at Alexandria's T.C. Williams High School, it's no big deal. Many of them had not even heard last week that they soon may be able to get free contraceptives at a city-sponsored clinic nearby. And those who knew weren't particularly excited.

"I've read about it in the paper, but you don't hear a lot of talk around here," said sophomore Michelle Lacey, 15. Added junior Brandon Bowers, 16, "It's not something you sit around and talk about at the lunch table."

For weeks, however, some of their parents and the city's entire political establishment have concentrated on little else but the proposed clinic. The long-running national debate over birth control and teen-age pregnancy has descended on Alexandria, and few except the teen-agers have held their passions in check.

On Tuesday, the Alexandria City Council and School Board will hold a public hearing on whether to open a "teen clinic" that would, among other things, distribute condoms and offer birth control advice. It would be located in or near T.C. Williams, the city's only high school, and would be the first public clinic of its kind in the Washington area.

Officials expect Tuesday night's hearing to be emotional and to carry over into Wednesday morning. A local group formed to fight the clinic is spending $7,500 on radio and newspaper ads, while a proclinic group is striking back with a smaller newspaper campaign of its own. The two sides cite contradictory academic studies on the effect such clinics have on pregnancy rates.

The Catholic Diocese of Arlington, which includes most of Northern Virginia, is opposing the clinic, and all of Alexandria's Catholic churches are expected to raise the issue in masses today, Monday and Tuesday. The anticlinic forces have formed a political action committee that they say will "screen City Council and mayoral candidates" on the issue before city elections next May.

Indeed, the clinic looms as a substantial campaign issue. Mayor James P. Moran, a Democrat, is one of the clinic's outspoken proponents; Republican City Council member Carlyle C. (Connie) Ring Jr. is a prominent critic and is considered the GOP's leading mayoral contender. Moran and Ring have debated each other on the clinic question three times.

"Had I not gotten involved in the clinic matter, there would be no issue in next year's election," Moran said last week. "It's inevitable that this will be a major concern."

The rhetoric surrounding the clinic -- and the potential political fallout -- may have become more sweeping than its practical effect. Students already can get contraceptives and birth control advice through the city's Health Department, which operates a clinic across town from the school. And just a half mile from T.C. Williams, a private, nonprofit clinic in a Methodist church offers the same services.

But the Alexandria debate, like most political discussions involving birth control or abortion, has stirred a cauldron of emotional issues, including sex, religion and the sociological links between teen-age motherhood and the underclass.

Opponents say that putting a clinic inside T.C. Williams would confer tacit approval of birth control and encourage promiscuity. Proponents say that stopping "babies having babies" is one of the few ways to break the cycle of poverty.

"We don't sing hymns and pray in school like we did when I was growing up, and there's considerable justification for that," Ring said. "But neither is it appropriate for the values of a more secular society to be imposed on those with particular religious convictions. {The clinic proposal} attempts to address the teen pregnancy issue simply in terms of distributing contraceptives."

Moran counters, "I don't believe our young people are so impressionable or undisciplined that the availability of birth control is going to cause them to engage in sexual activity.

"Teen motherhood is the single most identifiable cause of poverty in this city. I am convinced {the clinic} is going to substantially reduce the number of pregnancies and abortions, and help our next generation."

Both sides agree on one issue: Alexandria has a serious teen pregnancy problem, and it is becoming worse. According to Virginia Health Department statistics, 485 city teen-agers became pregnant last year, and more than half had abortions -- both significant increases from the year before.

Almost 18 percent of Alexandria girls between 15 and 19 conceived in 1986, the highest teen-age pregnancy rate in Virginia. (Alexandria's rate is lower than that for the District of Columbia, where more than 17 percent of all teen-age girls gave birth. The District does not require health providers to report abortion statistics.)

Concern over the issue was already evident 18 months ago when a panel sponsored by the Alexandria United Way urged the city to dispense contraceptives through a clinic at T.C. Williams. But the proposal hit a wall of opposition and died immediately. Moran revived it in August of last year when he appointed a city task force to study the question in detail.

The task force grew to 41 members and has wrestled with politically loaded questions from the beginning. In its report, 24 of its members endorsed the clinic proposal; a half dozen opposed it. Some of those in the minority charged that the task force was nothing more than a kangaroo court.

The clinic "was a fait accompli with the task force. We were given the solution in the beginning and then used deductive reasoning to justify it," said the Rev. William F. Walsh, principal of Bishop Ireton High School, Alexandria's only Catholic high school for boys. Walsh serves on the task force and helped found Concerned Alexandrians for Responsible Education, the anticlinic group.

Walsh said that dispensing contraceptives at T.C. Williams "would be throwing gasoline on a fire" of teen-age promiscuity. He urged that public schools combat teen-age pregnancy through counseling and courses that encourage sexual abstinence. CARE has compiled a list of 30 such programs that are in use elsewhere.

But former City Council member Mel Bergheim, a founder of the proclinic Alexandrians for Teen Health, said the clinic's staff would include counselors to recommend restraint. He also said the clinic would monitor students' overall health, helping those who otherwise get no medical attention.

"If our thesis is correct, we should see a decline in teen pregnancy, a decline in sexually transmitted diseases and an increase in teen health generally," Bergheim said. "The key is proximity and access. The closer at hand services are, the more likely they are to be used."

Clinic advocates acknowledge that political pressure has made it unlikely that the proposed facility would be built on the grounds of T.C. Williams. Instead, they hope to put it a short walk away, possibly in the city's Chinquapin Recreation Center.

Plans call for a staff of one nurse practitioner and two counselors, and an annual budget of about $250,000.

Even if the proposal is defeated, it seems certain to follow Moran through next spring's elections. "You're darned right it is," Walsh said. "I voted for Mayor Moran last time, but not again. And some people who campaigned for him have told me the same thing."

Were he to run against Moran, Ring said, he would not campaign on the clinic issue. "I'm sort of in the middle on this thing," Ring said. "I personally have no problem with an individual addressing the problem {of teen-age pregnancy} by using contraceptives. But I think in a pluralistic society we have to have respect for everyone's opinions."

"I personally would not want to link" the mayoral race and the clinic question, Ring said. "There's nothing more frustrating in public life than one-issue people. And this thing cuts both ways. I'm not sure {opposing the clinic} is a winning issue."

Moran said that his mail is running about 20 to 1 against the clinic, but that his mind is made up. "I think the worst thing we could do is do nothing and pray that things are going to go back to the way they were 20 years ago," he said. "They're not.

"On some issues everybody feels strongly, and this is one of them. You simply have to do what you think is right."