Administration officials and leaders of the president's Social Security Advisory Commission indicated yesterday that they may be closing in on a compromise to save the giant system after further talks were held in Blair House and President Reagan was briefed on the alternatives on his way home from a speech in Dallas.

While both sides said they were close, however, both also said the talks could still blow up in disagreement.

One commission member said after last night's talks there was tentative agreement on all but a few provisions. If these can be cleared up today the full plan will then be put to the president and House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.). If they concur it presumably will be made part of the president's upcoming fiscal 1984 budget.

But another member cautioned that the tentative agreements were "fragile" and "hanging by a thread."

The compromise under discussion involved a speedup of Social Security tax increases already scheduled for 1985 and beyond; partial taxation of Social Security benefits for those over certain income levels; a delay in future cost-of-living increases in benefits; and inclusion in Social Security starting next year of all new federal workers and all federal workers with fewer than three years of service.

Democrats and Republicans on the divided advisory commission have agreed that the system needs an extra $150 billion to $200 billion between now and 1989 to stay solvent. Republicans have favored raising most of this through benefit cuts; Democrats, through tax increases. The compromise would do some of both and raise $160 billion to $170 billion over the next seven years.

Those involved in the talks last night included Senate Finance Committee Chairman Robert J. Dole (R-Kan.), commission Chairman Alan Greenspan, Sen. Daniel Patrick Moynihan (D-N.Y.), former Social Security commissioner Robert Ball, and White House officials James A. Baker III, David A. Stockman, Richard Darman and Ken Duberstein.

The advisory commission must make its report by this Saturday, and the negotiators were trying in any case to agree on a compromise in time to have it put into the budget now under preparation, which is scheduled to go to Congress Jan. 31. Social Security tax increases and benefit cuts would help considerably in reducing projected deficits next fiscal year and further into the future.

But as well as having substantive differences, both sides have feared the political consequences of taking the lead with a proposal.

The compromise under discussion would not only virtually wipe out the system's short-term deficit over the rest of this decade, but the long-term deficit forecast for the next century, when the ratio of older people to workers will be much higher than now.

The main elements of the compromise:

Take into the system all new federal workers and those with less than three years of federal service as of Jan. 1, 1984, and all employes of nonprofit organizations not presently covered. They would have to pay the full tax and would be eligible for all benefits. Federal employes are now mostly exempt from the system--they are required to pay only the Medicare part of the tax--and nonprofit organizations can join or not as they choose.

Require self-employed people to pay the same tax on their earnings that an employer and employe combined would pay on the same amount of wages. At present, the self-employed pay only three-quarters of that figure.

Impose the federal income tax on half the benefits of all single Social Security recipients with total incomes from all sources of $20,000 or more. For married couples filing jointly, this cutoff would be $23,000 or perhaps $25,000.

Accelerate Social Security tax increases already scheduled for 1985 and 1990. The 1985 increase would be imposed in 1984, and half the 1990 increase in 1988. Workers would be able to offset these added taxes by taking credits against their income taxes. In effect this would shift the financing burden from the Social Security to the income tax.

Delay this year's scheduled July 1 cost-of-living increase by six months, or delay it three months this year and then a month a year for the next three years.

Eliminate the so-called "windfall" portion of Social Security benefits now received by federal employes who work in the private sector only a short time.

Starting in about the year 2010, gradually reduce basic benefit levels so that, for an average worker retiring at age 65, the first Social Security check will eventually equal 40 percent of the last paycheck instead of 42 percent as it does now.

Make the Treasury repay Social Security immediately for about $13 billion in free Social Security credits extended in the past to members of the armed forces.

Starting in the year 2000, provide that people retiring early at age 62 receive benefits 24 percent below what they would have received had they waited to retire at age 65. This amounts to a reduction of 8 percent per year for early retirement instead of the current 6.6 percent. Persons delaying retirement past 65 would receive a bonus of 6 percent or 8 percent for each year of delay, instead of the current 3 percent.

In a related development, the Social Security Bulletin reported that the majority of aged households rely on Social Security for at least half their income, and for the poorest households it provides 79 percent of total income.