Strong opposition began to surface yesterday as the Senate Rules Committee, under a mandate to complete action by Jan. 19, opened hearings on a proposal to slash the number of Senate committees from 31 to 15 in order to streamline the chamber's operations.

Major objections came from senators whose committee jurisdictions would be weakened, or who support veterans, the elderly and other groups in attempting to preserve special committees looking after their interests.

Many on Capitol Hill see the reaction as a forerunner of the opposition that will be weakened, or who support veterans, the elderly other groups in attempting to preserve special committees looking after their interests.

Many on Capitol Hill see the reaction as a forerunner of the opposition that will greet President-elect Jimmy Carter's plan to reorganize the executive branch when it reaches Congress.

The reorganization proposal, which is designed to reduce each senator's work load and end overlapping jurisdiction among committees, would cut the number of standing, special and joint committees to 15 and reduce subcommittees from 174 to 100. Functions of abolished committees would be redistributed.

For a moment all was good feeling and praise as committee chairman Howard W. Cannon (D-Nev.), senior Republican Mark O. Hartfield (R-Ore.) and Senate Majority Leader Robert C. Byrd (D-W. Va.), heaped compliments on Sen. Adlai E. Stevenson (D-Ill.) and other members of his special study committee for their work in drafting the committee reorganization proposal.

Then the witnesses took the stand, and while praising the general concept, began raking over the details.

Sens. John J. Sparkman (D-Ala.) and Clifford P. Case (R-N.J.) told the committee they didn't like proposals transferring control of some portions of international economic policy from the Foreign Relations Committee, of which they are the leaders, to the Banking Committee. Sparkman said further that he didn't like giving joint jurisdiction over foreign military sales to the Armed Services Committee, and he added that he also opposes abolishing the Joint Economic Committee and distributing its functions to other units.

Sen. Clifford P. Hansen (R-Wyo.) and Strom Thurmond (R-S.C.) said they like the overall reorganization proposal but would refuse to go along with abolishing the Veterans' Affairs Committee.

"The 1977 VA budget exceeds $20 billion," said Thurmond. "The agency employs 226,000 individuals - more than any other executive department except defense" - and operates a huge medical care system with 171 hospitals. How, he pleaded, could an agency of such huge size be denied a committee in Congress to handle its affairs?

Harrison A. Williams Jr. (D-N.J.), a Rules Committee member, said he opposes abolishing the Senate Special Committee on Aging, which he said does valuable studies and investigations that lay the groundwork for legislations by the labor committee, which handles actual legislative bills on aging. Abolition of the Aging Committee is strongly opposed by the National Council of Senior Citizens and by committee chairman Frank Church (D-Idaho), who has vowed to lead a fight to preserve the unit.

Hatfield' summarizing why the reorganization proposal is going to have difficulties even though everyone thinks it's a good idea in the abstract told his colleagues that "veterans, small business, postal groups and the aging," all have strong reservations about the provisions abolishing the special or legislative committees on veterans, small business, post office and the aging.

"They feel their interests are not going to be looked after", he said, saying he has received heavy constituent mail on the subject.

The fears of interest groups that they will lose their special access to Congress are only part of the hurdle faced by the committee proposal. The other part is rivalries between existing committees for jurisdiction over certain subjects. This was illustrated by the Sparkman-Case remarks, and by Thurmond's statement that he opposes transferring Panama Canal jurisdiction even in part to the Commerce Committee instead of Armed Services, or letting Armed Services give up jurisdiction over U.S. petroleum and oil shale reserves, or overseas schools for soldiers' children.