The House Ways and Means Committee began work yesterday on the bipartisan Social Security rescue plan amid signs that the plan is starting to pick up support from major business groups and organizations of the aged.

Commission Chairman Alan Greenspan told the committee that knocking out any of the major elements of the plan could unravel the package and destroy the delicate political agreement that led to its endorsement by both President Reagan and House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.). These major elements would provide $168 billion over the next seven years to keep Social Security solvent, and would eliminate about two-thirds of its long-term 75-year deficit.

Speaking for the 12 members of the special presidential commission that approved the package two weeks ago, Greenspan said that "all of the individual components" of the agreement were distasteful and "negative" in some degree to each of the 12, but "we support them" as a package because they help solve the Social Security financing problem.

During the testimony, it became clear that one major issue facing the committee and Congress, how to cover the one-third of the long-term deficit that the bipartisan package does not cover, promises to be the biggest conflict between Democrats and Republicans.

Greenspan and several other members of the commission called for a gradual rise in the retirement age to 66 after the turn of the century, and then periodic rises based on increases in life expectancy.

That would wipe out the rest of the long-term deficit, but the five commission members appointed by Democratic congressional leaders, represented yesterday by former Social Security commissioner Robert Ball, and several Democrats on the Ways and Means Committee, such as James M. Shannon (D-Mass.), said they strongly prefer an increase in the Social Security payroll tax in the year 2010 if necessary.

Several organizations of the aging said yesterday that they dislike the proposal to raise the retirement age.

Ways and Means Chairman Dan Rostenkowski (D-Ill.) declined to say which option he prefers.

"I don't intend to move my head or blink my eyes," he told reporters, but he added that he is "very optimistic" about the major proposals offered by the commission majority.

The package was strongly supported by four other commission members in addition to Greenspan--Robert Beck, chairman of the Prudential Insurance Co.; National Association of Manufacturers President Alexander Trowbridge; businesswoman Mary Falvey Fuller, and Ball.

Beck told the committee that the Business Roundtable, which includes about 200 business organizations, "supports the compromise plan in its entirety," adding: "The alternatives are just horrible." He said the American Council of Life Insurance, spokesman for the life insurance industry, also endorses it.

Trowbridge told a reporter "I'm reasonably confident the NAM will endorse it on Friday," when its board meets.

Meanwhile, the proposal won backing yesterday for the first time from a major national organization of the aged, the National Council of Senior Citizens. In a news release distributed at the hearing, the council called the plan "generally acceptable," although the release said it does not like the proposed six-month delay in this year's cost-of-living adjustment and hopes "there is some way to ease the hardship."

Two of the three commission members who opposed the bipartisan plan, former representative Joe D. Waggonner Jr. (D-La.) and Rep. Bill Archer (R-Tex.), said the economic assumptions used by the commission were "overly optimistic."

"I'm telling you now you can't fix it with what the commission has recommended," Waggonner said.