The city's summer jobs program apparently overcame a major financial obstacle yesterday through a maneuver that will allow an additional 8,564 teen-agers to begin working July 9 and be paid without Congressional approval of a special budget that includes money for their wages.

Sen. Charles McC. Mathias, ranking minority member of the District appropriations subcommittee, said the city will allowed to use money from previously approved budgets to pay the teen-agers while the $7.3 million special appropriation goes through Congress.

Gladys Mack, the city's budget director, said Mayor Marion Barry has accepted Mathias' offer and will ask the City Council Monday to approve a formal request to the Congress to shift city money temporarily to pay for the summer jobs.

Money borrowed from the city's treasury would be repaid when Congress as expected approves the money for the summer jobs.

Yesterday, meanwhile, was to be the first day at work for 18,500 teen-agers who also are in the city's summer jobs program. For most of the youths it was an orientation day with little or no actual work but several stern lectures from supervisors. The girls were told not to wear halter tops and see-through blouses on their new jobs and all the youths were urged to be responsible and work hard or risk being fired.

"Do you know what CPT is?" Dr. Richard Fairley, director of the division of education for the disadvantaged at the U.S. Department of Health, Education and Welfare, asked about 465 teen-agers who attended one of several orientation sessions around the city.

"Do you know what EST is? EST is Eastern standard time, CPT is colored people's time, and it's 10 minutes after everybody else's [time]. Be punctual." said Fairley, who is black.

At Stanton Dwellings in Southeast Washington, a public housing project where teen-agers working for the city's housing department will be repairing doors, painting apartments, and helping in the recreational center, only 68 of 114 youngsters who were assigned to work there showed up for work yesterday.

"I'm disappointed that so many youths would go through all the paper work and not show up for the jobs," said William Duckette, assistant manager of Stanton Dwellings.

At one orientation session around the city there was a similar smaller-than-expected turnout for the summer jobs program.

James F. Tompkins Jr., director of the department of recreation's swimming pools, said the light turnout may be due to several changes during the last six weeks in the starting date for the summer jobs program. Tompkins said the program first was scheduled to start June 25, then June 2 and finally June 28. He said the changes may have confused youngsters.

Hundreds of teen-agers continued to call job counselors at the citys' 12 senior high schools yesterday to say they have not been notified where they are to report to work. Some of those youngsters, the counselors said, do not understand that they will receive notices in the next week because their jobs do not start until July 9.

"I've had over 75 calls [since 8 a.m.] from kids saying they don't know where they are supposed to go," Doia Lawson, head of the youth employment center at Roosevelt High school said at 11 a.m. yesterday. "I want to tell them all to call the mayor but I can't."

Staff members of the District subcommittee said the offer to the city to reprogram other funds temporarily for summer jobs is a clear signal that passage of the special appropriatons is expected by Mathias and subcommittee chairman Sen. Patrick J. Leahy (D-Vt.).

Rep. Charles Wilson (D-Texas), chairman of the House subcommittee that deals with the city budget, has announced his support for the full summer jobs program.

If the city is able to get funds for the 8,654 jobs it will be within approximately 4,000 jobs of reaching the mayor's goal of 30,000.

"As soon as mayor Barry asks us, we'll approve the transfer (of money from other city budgets to the summer jobs program)," Mathias said. "This will help to get the District government through the next two or three weeks, which are critical in meeting the employment needs of young people. It will help put them in jobs immediately instead of waiting the two or three weeks it will take to get the supplemental appropriations bill approved by both houses of Congress." CAPTION: Picture, SEN. CHARLES McC. MATHIAS . . . removes jobs obstacle