Economist Alan Greenspan, chairman of the National Commission on Social Security, said yesterday that the group may be able to reach a bipartisan consensus by its Jan. 15 deadline on how to save the Social Security system, but not without guidance from President Reagan and House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.).

Greenspan, chief economic adviser to President Ford, said there is a "desire on the part of all" 15 members of the panel to come forward with a set of recommendations designed to accelerate scheduled Social Security tax increases and reduce mandated cost-of-living benefits increases.

But Greenspan, interviewed on "Meet the Press" (NBC, WRC), said he doubts that the sharply divided commission will agree on a solution to the $150 billion to $200 billion Social Security system funding shortfall expected between 1983 and 1989.

The 10 Republicans appointed to the commission lean more toward cutting benefits to ease the system's financing problems, while the five members named by Democrats favor increasing Social Security taxes.

The system is sending checks to older Americans faster than it takes in funds from taxes. To cover checks during the last two months, the old-age fund has borrowed $17.5 billion from trust funds in the Social Security system that pay Medicare and disability benefits.

Greenspan said commission members are "surrogates" for political decision-makers and "reflect the deep-seated differences" on how the massive income maintenance system should be saved. The commission was scheduled to expire Dec. 31, but President Reagan extended its life until Jan. 15.

Although other panel members, as well as Senate Finance Committee Chairman Robert J. Dole (R-Kan.), have said the commission cannot reach consensus unless O'Neill and Reagan provide guidelines on what they would find acceptable, yesterday was the first time that Greenspan has said the president and speaker are the key to such a consensus.

Administration sources have suggested that Reagan is signaling his willingness to consider tax increases as part of a bailout, while O'Neill apparently has sanctioned a compromise proposal that postpones benefits increases for three months. But sources close to O'Neill said there have been no behind-the-scenes negotiations between him and Reagan.

Problems facing the Social Security system are so great, Greenspan said, that some form of agreement clearly must be struck to make the system financially solvent.

Whether the solution will be found "in the context of the commission or through the legislative processes . . . is not clear. A lot of people, both Democrats and Republicans, think it would be easier in the context of the commission," which brings all factions together at the same time, Greenspan said. "Whether that is achievable as yet remains to be seen."

Several weeks ago, Greenspan said he thought there was no hope of finding a compromise position among the 15 members. But yesterday, he said he would have to "back off that statement slightly."

If no consensus is found, Greenspan said he prefers that the commission list options Congress must consider and areas of agreement and disagreement, rather than issue majority and minority reports that might further polarize positions on the Social Security question.

Whether the commission reaches a compromise position or not, any changes in taxes or benefits must be approved by Congress.