Enough members of Congress were finally found yesterday to serve on the House District Committee that oversees this city, a committee that is hardly the most popular assignment on Capitol Hill.

None of the 48 new House Democrats heretofore had volunteered to serve on the District Committee, but only after the Democratic caucus voted to change certain committee membership rules as a sweetener.

Democrats nominated to serve on the District Committee were Reps. Theodore M. Risenhower (Okla.), Fortney H. Stark (Calif.), Charles Rose (N.C.), Norman E. D'Amours (N.H.), Douglas Applegate (Ohio) and Leon E. Panetta (Calif.). Only the latter two are freshmen.

Full membership was found for the committee only after the House Democartic caucus voted a change in the rules to allow members to serve on it as well as two other standing committees.

The standing House committees are designated as either "major" or "nonmajor." Tactfully, none is called minor. Congressmen are allowed to serve on one major or two nonmajor standing committees.

To encourage recruits for the House District Committee is suddenly a major committee, just that its status is sufficiently confused so that the new members can serve on it as well as on the committee they really want to be on .

The District Committee's membership has been reduced from a previous authorized total of 25 to 19 - 13 Democrats and six Republicans, not including D.C. Del. Walter E. Fauntroy (D), now third-ranking Democrat.

Rep. Charles C. Diggs Jr. (D-Mich.), chairman of the House District Committee, noted yesterday that it "was not the only one that had recruiting problems." The House leadership also had to use some friendly persuasion to fill vacancies on the Judiciary. International Affairs and Agriculature committees.

The District Committee is of little interest to most congressmen largely because Washington is a long way from their congressional districts and Washington residents are not coting constituents.

With home rule, the District Committe has little legislative function but reviews District government actions. Diggs said his prime objective for the committee this session will be to promote the city's economic development.