As congressional conferees passed the $33 billion mark in resolving differences over spending cuts, Democratic and Republican leaders yesterday disclosed a bipartisan agreement to soften the impact of one of the most controversial provisions: repeal of the minimum Social Security benefit.

Although no details were worked out in informal talks over the last few days, spokesmen for Republican leaders said they intend to try to work out a bipartisan solution to the issue, which has turned into a political briar patch for the GOP.

"We're in general agreement that something should be done for those who fall between the cracks," said an aide to House Minority Leader Robert H. Michel (R-Ill.).

First word of the behind-the-scenes talks came from House Budget Committee Chairman James R. Jones (D-Okla.), who told reporters that Republican leaders had agreed with Democrats on the need for separate legislation to correct "inequities" stemming from elimination of the $122-a-month benefit for those now receiving it.

"There is bipartisan recognition that something has to be done for those who rely on the minimum benefit," said Jones.

Spokesmen for Michel and Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) agreed with that statement but emphasized that an eventual compromise may involve something other than restoration of the benefit, which goes to 3 million people who have not worked long enough to qualify for full Social Security retirement benefits.

In a speech earlier this week, Michel suggested changing the means test for Supplemental Security Income so that SSI, which is a form of welfare for the aged, blind and disabled, will protect the poorest of the minimum benefit recipients from any income loss.

But an aide to Baker said this may not be enough, a point also made by many Democrats, who want to see the benefit restored as part of Social Security, at least for current recipients. "There's some concern up here that SSI is just another form of welfare" that many older people may be too proud to seek, said the Baker aide.

Vague as it may be, the Republican move toward a bipartisan agreement -- coming just days after President Reagan called for a bipartisan solution to the whole Social Security financing problem -- underscores the GOP jitters at the constituent backlash that the party is getting from Reagan's proposals for Social Security cutbacks.

There are some Democrats who would like to see the Republicans twist in the wind a while longer on the issue, although they are under pressure to move, too, because they've made such an issue of the minimum benefit.

Both houses approved elimination of the benefit for current as well as future recipients as part of their budget "reconciliation" legislation cutting nearly $40 billion from domestic spending programs, now getting its finishing touches in a massive House-Senate conference. Conferees agreed Thursday to end payment of the minimum benefit for new retirees after December and for current beneficiaries as of next March. The administration which favors the full cut, estimates it will save about $7 billion over the next five years.

But, with thousands of old people protesting on the Capitol steps, the House voted overwhelmingly earlier in the week to find a way to restore the benefit for those currently receiving it. Even though the Senate refused to go along, the House vote "helped get us off dead-center," said a Senate Republican leadership aide.

The House Ways and Means subcommittee on Social Security may take up the issue as early as the end of next week, sources said, although the March cutoff for benefits to current recipients gives Congress some breathing time.The subcommittee has already recommended keeping the benefit for current recipients.

In related action, the Senate voted 89 to 4 for a "sense of the Senate" resolution urging its Finance Committee to draft legislation aimed at solving the Social Security retirement fund's immediate cash-flow programs by permitting borrowing from the solvent disability and Medicare funds. This would relieve some of the pressure for big Social Security cuts, although it would not solve long-term problems.

As the 58 separate subconferences on the spending cuts moved toward completion, theoretically early next week, Medicaid conferees were reported moving toward dropping the administration's proposed "cap" on the growth of Medicaid in favor of a more flexible target to limit spending. A Senate provision reducing the minimum federal payment from 50 percent of a state's Medicaid outlays to 40 percent, which would have meant cuts for the District of Columbia and Maryland, was also considered likely to be dropped.

Another set of conferees agreed to a dairy price support program that Agriculture Secretary John R. Block has said is unacceptable. It establishes milk prices supported through government purchase at 75 percent of parity, while the administration favors 70 percent. But the conferees agreed that dairy support will be reconsidered this fall when Congress considers renewal of all government commodity price support programs. The farm cuts approved by the conferees totaled $1.6 billion.