Getting a summer job with Uncle Sam is going to be tougher than usual this year.

Although hundreds of thousands have applied for jobs as summer clerical aides or through the stay-in-school program for needy youth, only a relative handful of lucky or well-connected persons will get them this year thanks to budget cuts, coming layoffs of regular employes and lack of interest from the administration.

More people than ever are trying to get June through September jobs because the government has done away with proficiency tests for typing, stenography and other clerical skills.

In a good year -- which this is not -- Uncle Sam hires about 114,00 summer workers. Most are "needy" youth. They are certified for the stay-in-school program by state employment offices.

Federal agencies in metropolitan Washington usually hire between 13,000 and 14,000 students -- about half of them from low-income families -- to help them earn money for school.

This year, agency hiring offices estimate that only between 9,000 and 10,000 people will be hired for summer jobs.

Because the office skills test was abolished students were allowed to certify themselves as qualified typists, and the like. As a result, more people than ever have applied to agencies at a time when the actual number of vacancies is much lower than usual. In the past, federal agencies have been encouraged by the White House to hire one needy student for every 40 regular employes.

President Reagan will send agencies a message within the next few days telling them to support the stay-in-school program. But that message probably will not stress the 1-for-40 goal.

It is too late to apply for most of the summer jobs. Cutoffs varied by agencies. Some applications had to be in by Feb. 15, but the last date for applying in most cases was April 15.

All of the above means a bleak summer job picture this year. This at a time when local industry is also belt-tightening, and many students and families are hard-pressed to come up with high school and college money.