TOMORROW - thanks to exceptionally vigorous responses from the District government, congressional committees and the business community - the first wave of an estimated 30,000 city youngsters will report to summer jobs. The rest are expected to start work by July 9. That would mean that Marion Barry's campaign pledge last year to double the number of summer jobs for young people had been fulfilled.

Yet neither the government nor the private sector can relax, for more needs to be done. Thousands of teen-agers still face the bleakness of a summer without a job; whatever additional work can be offered should be. As for those jobs that have been offered, how many really will be filled - and how will they work?

Already there have been paperwork difficulties. One reason the city government cannot start all the jobs this week is that it has had to wait for the formal congressional approvals and presidential signature permitting the hiring of about 8,500 youngsters. However inefficient and unfair this congressional appropriations requirements is, on this occasion the key leaders - Sen. Patrick J. Leahy (D-Vt.) and Rep. Charles Wilson (D-Tex.) - did act with sympathy and dispatch, even though they were unable to schedule the final congressional approvals before the Fourth of July break. Besides, it was a late request by the city, because the Barry administration only took office in January.

City administration officials also held up the start of some jobs for a good reason: They wanted to make sure the youngsters would get paid on time - and a check showed that the payroll system wouldn't handle it. Rather than have to postpone the first payday for teen-agers - many of whom would have spent lunch and transportation money - officials decided to start a portion of the eight-week jobs a bit later. Again, that makes sense this year, since things were a bit rushed. But just as the jobs effort must get moving earlier, the payroll system must be adjusted.

More needs to be known, too, about how many of the private-sector job offers materialize. This summer, the Metropolitan Board of Trade and other participating business groups should take a closer look at the responses to their program, including getting specific reports from employers on the numbers and performances of youths hired. In addition, the private campaign may need some revision to make sure that employers' job offers are indeed tight commitments to accept referrals from the area governments' agencies.

No summer jobs effort can guarantee satisfying, lucrative, constructive work for every teen-ager in town, nor can the government be the primary employer. But much has been learned this spring about how to run a better program than last year - and the momentum should not be lost.