ARLINGTON, Va. -- Once a month, in a windowless office near the Pentagon, specially trained federal employees roll two lottery machines out of a closet to practice something the government has not had to do in more than 40 years: selecting young Americans for the military draft.
Following strict written procedures, they power on the machines, and 366 table tennis balls -- one for every day of the year, including for leap year -- clatter around for five minutes, the time government mathematicians have determined will ensure the balls are properly mixed.
Then, as in a Powerball drawing, one of the employees hits a button that shoots a ball through a small pipe to the top of the machine, where the director of the United States Selective Service System pulls it out.
''January 25th, January 25th,'' the director, Lawrence G. Romo, called out on Friday as he displayed the front of the ball to an empty room in front of him.
Mr. Romo then walked over to the second lottery machine, which produces numbers that assign the order in which those born on that day would be drafted. For the occasion, Mr. Romo -- who reports directly to President Obama but has met him only once, to shake his hand and pose for a photo -- wore a suit and an American flag tie.
After decades of work far from public attention, Mr. Romo and his staff are now facing what could be the most significant change to their sleepy agency in decades.
With the Defense Department opening combat roles to women, the Marine Corps commandant, the chief of staff of the Army and one of the top Democrats on the Senate Armed Services Committee said last week that women should be required to register. Two days later, two Republican members of the House who are military veterans -- Duncan Hunter of California and Ryan Zinke of Montana -- introduced legislation that would require women to register.
''I know women play an invaluable role in war,'' Mr. Zinke, a former member of the Navy SEALs, said in a statement released by his office that announced the legislation. ''My daughter was a damn good Navy diver. Many times women can gain access to strategic sites that men never could.''
Defense Secretary Ashton B. Carter said Congress should study the issue. The White House has not taken a position. Asked at a Democratic candidates debate, Hillary Clinton said she would need more information before deciding.
Some Republican presidential candidates, including Senator Marco Rubio of Florida, have said they favor requiring women to register with the Selective Service, while Senator Ted Cruz of Texas said on Sunday at a forum in Peterborough, N.H., that he opposed it.
''Political correctness is dangerous,'' Mr. Cruz said. ''And the idea that we would draft our daughters to forcibly bring them into the military and put them in close combat, I think, is wrong. It is immoral, and if I am president, we ain't doing it.
''I'm the father of two little girls,'' he added. ''I love those girls with of all my heart. They are capable of doing anything in their hearts' desire. But the idea that their government would forcibly put them in a foxhole with a 220-pound psychopath trying to kill them doesn't make any sense at all. And it's yet one more sign of this politically correct world where we forget common sense.''
For the moment, the discussion has cast attention on the Selective Service, resurrecting for baby boomers memories of the Vietnam War, and leading some millennials to wonder what the agency is and whether they ever registered with it, as required by law.
Typically, the agency has been in the news only when it has divulged whether presidential candidates registered for the draft. On Friday, the most pressing issue in the office was a request that had come in about the registrations of Mr. Rubio and Mr. Cruz, officials said.
The draft was last used in 1973, after it had compelled hundreds of thousands of men to fight in Vietnam. Since 1980, all men ages 18 to 25 living in the United States -- including those who are not citizens -- have been legally required to register with the Selective Service. President Jimmy Carter reinstituted the measure in response to the Soviet invasion of Afghanistan.
While those who do not register can be prosecuted, Richard Flahavan, an agency official since 1986 and its spokesman, said he knew of no convictions since a handful in the early 1980s.
But some consequences for not registering would most likely extend to women if they were included. Under the law, those who do not register can be denied federal jobs, security clearances, education grants and citizenship. In most instances, men are provided a chance to register and are then given the jobs or grants.
Citizenship issues remain. According to United States Citizenship and Immigration Services, if a man age 18 to 25 ''willfully'' decides not to register for the draft, his request for citizenship can be denied. If the man is between 26 and 31 and knowingly did not register, the citizenship can be delayed until he is 32. Officials estimate that this affects only a handful of men a year.
Most do register as required. According to the Selective Service, 88 percent of men in the United States ages 18 to 25 in 2014 were registered for the draft. The states with 99 percent compliance -- Florida, Idaho, Louisiana and Utah -- have programs that require men applying for their driver's licenses to sign up. Jurisdictions with the lowest compliance are the District of Columbia, at 34 percent; North Dakota, at 57 percent; and Vermont, at 58 percent.
While the idea of requiring women to register for the draft gained significant public attention only in recent weeks, officials at the Selective Service had been planning for it since the Pentagon announced in December that it was opening combat roles to women.
In January, the White House Office of Management and Budget called the agency and asked it to come up with an estimate for how much it would cost to register women. The agency -- which has a budget of roughly $23 million, the equivalent of what the Social Security Administration spends every 15 minutes -- said it would need about $8.5 million more for the first year of women's registrations and slightly less in the following several years. It would also need to hire several dozen employees.
The agency's officials said they needed to be prepared for legislation to reinstate the draft. Because the futures of so many Americans would be in their hands, they know that every move they would make during the ball selections would be broadcast live, and closely scrutinized.
PHOTO: Lawrence G. Romo, the Selective Service System director, with the lottery balls for a draft. (PHOTOGRAPH BY LEXEY SWALL FOR THE NEW YORK TIMES) (A17)