WITH SOME EXTRAORDINARY understanding and leadership from Rep. Charles L. Wilson (D-Tex.), about 8,500 District teen-agers may join the ranks of the employed when the city's critical summer jobs program officially begins a week from tomorrow. As of now, the eager young applicants are ready and so are the jobs - but the necessary congressional approvals are not. Things are beginning to move on Capitol Hill, though, and the response may well permit the elected government of this city to spend its own locally raised revenues in time to help the teen-agers. If so, it looks as if the local government, private business, labor and individual citizens will meet and - perhaps - surpass Mayor Barry's goal of providing at least 30,000 jobs for city youngsters this summer.

Here's how things stand and what still has to happen: Thanks to Sens. Patrick Leahy (D-Vt.) and Charles McC. Mathias Jr. (R-Md.), a Senate subcommitee's approval last week of the 8,500-job program won full committee approval on Monday. Efforts are under way to bring the proposal to the Senate floor as soon as possible - which is the cue needed for action in the House. Rep. Wilson, who heads the sub-committee in the House, already has scheduled a hearing for Friday; with a strong push by the chairman, House approval could come by next week, when the summer jobs program starts.

Still necessary - as part of the horrendously complicated, overly restrictive budget-approval process imposed on this city - would be President Carter's signature. But with an informal agreement by congressional and White House leaders on the summer jobs, City Hall could go ahead and put the teen-agers to work on time.

As of yesterday, including the 8,500 jobs awaiting congressional approval, the city government's count of offers from all quarters stood at about 28,235. If the private sector can see fit to come up with another 1,800 to 2,000 jobs, the city will have risen to the challenge. Even that will leave much more to do, for there are more than 50,000 teen-agers seeking work this summer. In the long run, it is private business, not government, that should take the major responsibility as well as reap the benefits of hiring eager local talent.