Democrats on the House Committee on Aging said yesterday that eliminating the Social Security minimum monthly benefit could cost the government nearly $2 billion more in welfare and Medicaid outlays over the next five years than it will save by killing the benefit.

Rep. John Burton (D-Calif.), presiding at a hearing of the retirement income subcommittee, said that the "hidden costs" of wiping out the minimum guarantee for 3 million persons now on the rolls were disregarded when President Reagan proposed eliminating the benefit and Congress, in last summer's budget bill, agreed.

He said the administration assumed that while 600,000 people would become eligible for welfare when the Social Security minimum benefit was eliminated, only about one-quarter of them would apply. Based on that, Burton said, the administration figured that killing the minimum would save the Social Security trust fund about $6.8 billion over five years and with only one-quarter of the 600,000 shifting to welfare, the net saving for the government as a whole would be about $1 billion a year.

However, Burton said calculations by the subcommittee staff show that if all 600,000 people shifted, it would cost the federal government $8.74 billion in added welfare and Medicaid outlays from 1982 to 1986, or about $2 billion more than the amount saved by eliminating the minimum.

In addition, he said, staff calculations estimated that the states would have to pay out an additional $1.4 billion for welfare over the period.

Burton and others also said that President Reagan's proposal to postpone the 1982 cost-of-living adjustment from July 1 to Oct. 1 would mean that three months of inflation would simply be dropped out of cost-of-living calculations. They said the administration proposal would skip three months and simply calculate the new inflation figure back one year from the new date.

Meanwhile, Senate Finance Committee Chairman Robert J. Dole (R-Kan.) said last night that he has not given up hope of fashioning a major bipartisan bill designed to insure the financial soundness of the Social Security system. "I'm an optimist," he said.

He said he plans further meetings with leaders and colleagues on both sides of the aisle in the hope of working something out, and has scheduled a Finance Committee meeting for tomorrow to go over a list of major options for such a bill to get the committee's sentiment.

Sen. William Armstrong (R-Colo.) said he is pessimistic that a bill can be put together now in view of the decision of House Democratic leaders last week to put aside the Social Security bill in that chamber and to oppose all of Reagan's proposals for cuts.

Armstrong predicted that unless the Democrats change their stance, the only thing that might emerge from the Finance Committee would be a stop-gap bill allowing the financially troubled old-age insurance trust fund to borrow from the better-off disability and Medicare funds to get through its short-term financing crisis and perhaps restoring the minimum benefit to some or all of those on the rolls now.

Dole and Sen. John Heinz (R-Pa.) said after a meeting of Finance Committee Republicans yesterday that they believed the Social Security problem should be considered by itself and not made part of any general federal budget-cutting move, lest it appear that the main reason for cutting Social Security was to balance the federal budget, rather than to put the system on a sound financial basis.