Defense Secretary Caspar W. Weinberger, under pressure from other senior administration officials, told President Reagan yesterday that he will reexamine the Pentagon budget in search of possible cuts, well-placed sources reported.

The Weinberger pledge came at a morning meeting at which several of Reagan's advisers, including Office of Management and Budget Director David A. Stockman and senior White House staff members, argued that the president must find savings in his proposed five-year defense buildup if the administration is to bring down what one official called "eye-popping" deficits.

In a separate session yesterday--a hectic day in which the entire budget seemed to be back up for grabs only three weeks before it must be sent to Congress--House Minority Leader Robert H. Michel (R-Ill.) also told the president that he must develop some alternative to the anti-recession jobs and housing bills that Democrats are expected to propose when Congress returns Jan. 25.

An aide to Michel quoted him as telling Reagan: "Responding to the Democrats by being naysayers is not an adequate response from Republicans to people who are unemployed."

And in a third session, the president was given a description of possible initiatives to combat the unemployment rate, which was 10.8 percent last month. A new rate will be announced today. Officials were instructed to report to him after determining what the proposals would cost.

These meetings occurred amid intensifying pressure to bring under control deficits now projected to exceed $280 billion by 1988.

Reagan was said by senior administration officials to be seeking ways at least to show a downward trend in the likely deficits over the next five years instead of the rising trend now projected. At his Wednesday night news conference, Reagan said the large projected deficits in later years are "unacceptable."

An administration official said various alternatives now are under study to produce such a declining path. One would be to drop the scheduled indexing of income taxes after 1985, a provision included in 1981 tax legislation to prevent tax rates from rising more or less automatically each year as wages increase with inflation. Some in Congress have advocated this, but it could not be learned if it was under active consideration.

At yesterday's session with the president, administration sources reported that Weinberger first argued that defense budget cuts would impair national security. The president also has made this point in recent months.

But other administration officials, including Stockman, were said to have argued that the long-awaited economic recovery might be aborted by the likely deficits. These officials were reported to be pressing Reagan to modify his budget plans himself before sending them to Capitol Hill, rather than leave them to negotiations with Congress later.

Weinberger then agreed to go back to the Pentagon in a search for possible savings, the officials said. It was reported yesterday that he already had ordered Pentagon officials on a contingency basis to study ways of bringing down the Pentagon's 1984 budget by about $8 billion to $11 billion.

Weinberger's agreement to look for military budget savings does not mean that he has agreed with demands for defense cuts, officials said. But they saw the development as an important sign that the president now is paying attention to those economic advisers who have warned him about the peril of the deficit. "I think the president is listening," said a senior administration official.

The more urgent warnings about the deficit were sparked by a new set of projections of economic activity for 1983 and 1984 that were outlined to Reagan Monday along with the more pessimistic deficit estimates. Reagan and his aides were described as "taken aback" by the escalating deficits.

Last year, a similar battle was fought internally over defense spending. Reagan eventually compromised between Stockman and Weinberger, but the Pentagon largely escaped deep cuts that Stockman sought.

In his news conference Wednesday night, the president said he is willing to look at a possible stretchout of his Pentagon buildup, but he insisted that it not interfere with his larger goal of rearming America.

Although the deadline is fast approaching for submitting his budget to the printers, White House officials said Reagan is wide open to new deficit-cutting proposals in the final days of preparations.

The president yesterday met with his Cabinet Council on Economic Affairs for a review of alternative programs for fighting unemployment. These were part of a package developed previously that included a now-abandoned idea to tax unemployment benefits.

Among the possible proposals was one to create a "sub-minimum" wage for teen-agers, and ideas for relocating and retraining workers who have lost their jobs because of long-term declines in their industries.

No final decisions were made, but White House officials were instructed to price out some of the proposals, officials said. Previously, Reagan has threatened to veto Democratic public works jobs bills on grounds that they are nothing more than "pork-barrel" legislation, a point he made again at his news conference.

Yesterday, Michel told reporters the Democrats had "stacked" the House Banking Committee in such a way that approval of a housing and jobs bill seems almost certain. "When your opposition is seriously considering moving in a certain direction, what are you going to do about it?" he asked.

An aide said Michel last year offered similar advice on housing and jobs, which was ignored by Reagan, who vetoed legislation including Republican-sponsored measures to stimulate housing construction.

However, during the lame-duck session last month, Michel backed Reagan in opposing any job-creating efforts other than $5.5 billion in highway rebuilding work that stemmed from a nickel-a-gallon increase in the gasoline tax.

The Democrats have not drafted their anti-recession program for the 98th Congress, but it is expected to include elements of the $5.4 billion public works jobs package that was passed by the House during the lame-duck session but jettisoned at the last minute in the face of a promised presidential veto.

Michel's advice to Reagan, which also included an appeal for tax, regulatory and trade-related assistance for recession-crippled heavy industry, came during a meeting between Reagan and House GOP leaders on fiscal 1984 budget preparations.

Both Michel and Rep. Barber B. Conable Jr. (R-N.Y.), ranking Republican on the Ways and Means Committee, said the Republican lawmakers indicated strongly that defense would have to trimmed if social programs are to be cut again. But the House delegation agreed with Reagan on holding the line on tax increases, according to Michel.