The Senate, its members standing by in stunned silence, broke off action on President Reagan's proposed budget cuts yesterday after Majority Leader Howard H. Baker Jr. (R-Tenn.) reported that the president had been shot.

The Senate had just rejected, 39 to 55, an attempt by Democrats to restore $800 million for continued funding of minimum Social Security payments of $122 a month.

It also refused, by a vote of 71 to23, to provide $1.5 billion to fill the Stragtegic Petroleum Reserve next year. Reagan had called for $3.8 billion for the reserve, but the Senate Budget Committee chopped out $3 billion in anticipation of legislation to require alternative means of financing the stockpiling of oil.

Defeat of the move by Senate Majority Whip Ted Stevens (R-Alaska) to restore half of the money the Budget Committee had cut did not clear the decks of the oil reserve issue, however.

Still pending were proposals from Sens. Bill Bradley (D-N.J.) and James McClure's proposal would require across-the-board cuts in other programs to offset the cost of filling the reserve; Bradley's proposal anticipated no offsetting cuts.

It was not immediately clear what the lopsided vote against Stevens' proposal portended for the Bradley and McClure efforts. The Senate was in the midst of debate on Bradley's amendment when word came over radios and wire service news tickers that any attempt had been made on the president's life.

Sen. Donald W. Riegle Jr. (D-Mich.) led the unsuccessful effort to continue funding of the minimum Social Security payment for the estimated 3 million retirees who are now receiving it. Reagan has proposed eliminating the benefit for present as well as future recipients as of July 1, meaning that they would have their benefits recalculated to reflect their actual earnings histories.

Riegle contended that the move amounted to "taking a meat ax to Social Security" and Sen. David Pryor (D-Ark.) argued that the issue involves "thousands of people who are literally eating out of garbage cans to stay alive." But Sen. Bob Dole (R-Kans.) said all except 300,000 minimum-benefit recipients would continue to get as much, if not more, from other Social Security benefits.

Riegle proposed to recoup the $800 million to continue the minimum benefit by requiring comparable cuts in general government expenses such as travel, filmmaking and office supplies.

Meanwhile the House Social Security subcommittee, which last week approved a cutoff of the minimum payment for prospective retirees only, yesterdday tentatively approved three provisions designed to improve Social Security benefits for women -- a goal for which women's groups have long been battling.

One would provide higher widow's benefits for women whose husbands die several years beofore retirement age.

A second would split a couple's earnings records for benefit purposes at the time of divorce. with each then getting credit for half the earnings regardless of who had earned them. But it would apply only to couples married at least 25 years, and would not start being phased in before 1984.

A third would give women limited credit years toward Social Security benefits for child care when they work for some years and then spend other years bearing children and caring for them.