The Senate's first major attempt in 30 years to reorganize its sprawling committee structure - by chopping the number of committees from 31 to 15 - is in serious jeopardy. It may be substantially watered down in the Senate Rules Committee and on the floor, key senators said yesterday.

The plan was put together by a special committee in committees headed by Adlai E. Stevenson (D-Ill.). It calls for the elimination of all the joint committees, including joint atomic, and of such minor units as the veterans, space, ethics, nutrition, post office, small business, District of Columbia and aging committees, with their functions redistributed to the 15 committees that would remain.

A second key feature is to limit a senator in most cases to two committees and two subcommittees on each of those.

The idea is to reduce overlapping jurisdiction, rationalize committee functions so that four or five committees aren't dealing with the same subject, and end the situation in which some senators belong to four or five committees and 12 to 14 subcommittees each, and impossible burden on their time.

The need for some sort of reorganization was vividly illustrated yesterday when the Senate Rules Committee's final hearing on the issue had to be canceled because most of the committee members were absent - attending other committee meetings.

The Stevenson plan is foundering because of rivalries between committees for jurisdiction over favored subjects, and heavy lobbying by veterans, small business, government employees, senior citizens and related groups for preservation of the minor committees, which they regard as their special protectors.

Sen. George McGovern (D-D.D.), whose chairmanship of the Nutrition Committee would disappear if the plan went through unchanged, said, "I'd like to see this whole reorganization thing sidetracked for a while - even if they allow Nutrition to survive."

Vainly waiting for a quorum. Rules Committee Chairman Howard W. Cannon (D-Nev.), told a reporters that judging from the temper of his committee, it appeared that the small business, veterans, joint economic and ethics committees all would be retained in their current status as separate committee, rather than being absorbed into other units as called for by the Stevenson plan. Similar predictions came from rules members James B. Allen (D-Ala.) and Dick Clark (D-Iowa), earlier.

Clark said, "Certainly it (the reorganization plan) is in great trouble."

Stevenson said retention of these minor committees would severely harm the plan by making it impossible to rationalize and consolidate jurisdiction over certain subjects and by making it extremely difficult to hold down the number of assignments of each senator (the current average is 18 memberships per senator on committees and subcommittees).

Among the added jurisdiction problems are these:

The Foreign Relations Committee is furious at the proposal to transfer control of some international financial foreign aid institutions, like the international bank, to the Banking Committee. (It will probably win this one).

Leaders of the Commerce Committee aren't particularly interested in having it assume most jurisdiction over transportation and mass transit, and are very unhappy about giving up jurisdiction over oceans.

Public Works Committee leaders want to keep public roads authorization jurisdiction and not give it up to Commerce, and aren't too happy about becoming the consolidated central environment committee, which is expected to be an umpire between business and environmentalists and get kicked in the rear end, politically, by both.

Some northern Democrats want to take away welfare functions of the Finance Committee, which Stevenson left intact.

Still an added complication is the desire of the Republican Caucus, announced by Senate Minority Leader Howard H. Baker (R-Tenn.), on Tuesday, to use the committee reorganization plan as a vehicle for getting more GOP staff on the committees. The Republicans want a guarantee of one-third of committee staff down the line for themselves as part of the package. According to the Republicans, they have only 19 per cent of the staff on the space committee, 15 per cent on Agriculture, 16 per cent on Appropriations, for example.

The fight over the committee reorganization is far from over, and Cannon, Robert P. Griffin (R-Mich.) and others suggested that even if all the Stevenson recommendations aren't followed, there still could be substantial improvement in ending overlapping and reducing overstretching of assignments.

For example, even if some of the minor committees are kept, such as veterans' and small business, there would be fewer of them than now. A senator might still be limited to service on two major committees and one minor, with permission to serve on two subcommittees on each of the major and one on the minor.

This woulf reduce the total number of committees and reduce an individual's assignments, tough not as much as the Stevenson plan wants.

Griffin, chafing at being at a Rules meeting that was canceled for lack of a quorum, said, "Right now I'm supposed to be here, in France (he isn't a member but was interested in its hearing) and at Foreign Relations." It is conflicts like that that make him "inclined to support Stevenson as much as possible," Griffin said, though he expects the original plan will be altered as it passes through the Senate.

"But I suppose anything we do is better than what we've got," he said. And then he hurried off to one of the other meetings.