White House chief of staff James A. Baker III said yesterday that if the president's Social Security advisory commission fails to reach broad agreement on a complete Social Security rescue package, the Reagan administration might seek legislation to enact whatever proposals the commission does approve.

Other officials, amplifying Baker's statement, said the White House would also include any projected savings from these proposals in its fiscal 1984 budget request.

Baker's remarks, in a telephone interview from San Francisco, came as leaders of the commission and a White House team headed by Baker prepared to meet again today in a last-ditch effort to agree on ways to save the system. Baker is expected to brief the White House press on today's discussions.

The commission had been scheduled to file its final report today, but yesterday asked for an extension until Thursday.

President Reagan, in an impromptu news conference, told reporters: "If they're going to plan on a few more days before they come to . . . a decision, we'll give them those few more days or whatever time this takes."

He also emphasized that he would make no endorsement of any proposals "until I see what the entire thing is that they recommend."

The president, with considerable heat, also said he did not want the Social Security issue again made into the kind of "political football" that "frightened the life out of a great many senior citizens" when it was brought up more than a year ago.

"No one that I know in this government has any intention of taking away the checks that these people are getting. I have said it over and over again, but somehow it does not get as much attention as the lies that have been told by those who want to portray us as somehow out to destroy Social Security," Reagan said.

Until recently, the 15-member commission, headed by economist Alan Greenspan, had been badly split, with most Republicans favoring curbs on the growth of benefits to ward off insolvency for the giant system, and most Democrats favoring some form of tax increases.

For the past two weeks, Baker's White House team and a commission group including Greenspan, Sens. Robert J. Dole (R-Kan.) and Daniel Patrick Moynihan (D-N.Y.), Rep. Barber B. Conable Jr. (R-N.Y.) and former Social Security commissioner Robert Ball have been meeting privately to try to work out a compromise.

The result so far has been a tentative package totaling $165 billion in benefit cuts and tax increases over the next seven years (the commission has estimated that tax increases or benefit cuts of $150 billion to $200 billion over the seven-year period are needed to keep the system solvent). Even this package has not been fully approved by the negotiators and the White House.

Moreover, five commission conservatives say the tentative package contains too many tax increases and too few benefit curbs, and yesterday they began preparing recommendations of their own.

One, Sen. William L. Armstrong (R-Colo.), predicted that even if the Baker team and the commission leadership group reach a compromise today or within the next few days that is then endorsed by both the president and House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), it still would not receive more than a 9-to-6 or 8-to-7 majority in the commission.

Baker said that he does not have full authority in the negotiations to commit the president to any package and could do so only after showing him the final package.

Baker said he saw two possible outcomes to the final round of negotiations: an agreement approved by a substantial majority of the commission, which could then be shown to Reagan and O'Neill; or, lacking that, a decision to "proceed legislatively." He did not define what he meant by a substantial majority or say whether a 9-to-6 vote would be enough.

Proceeding legislatively, he suggested, would mean introduction by congressional members of the commission of legislation embodying whatever recommendations the bulk of the commission agrees on, plus any other recommendations the administration might wish to make.