House-Senate conferees reached the midpoint of their work on nearly $40 billion in spending cuts yesterday, agreeing on issues that included rejection of President Reagan's proposal to kill the Economic Development Administration (EDA) and non-highway programs under the Appalachian Regional Commission (ARC).

Working late into the night in a tough bargainig session, Public Works Conferees agreed to retain $290 million for the EDA and $215 million for the ARC, including $50 million for Appalachian programs other than highways.

The Senate had proposed $50 million to phase out the EDA, which helps localities build industrial parks and other inducements for economic development. The House had proposed $360 million for the EDA.

Although the Public Works conferees and several other panels substantially were impasses on such touchy issues as food stamps and family-planning grants. And there was no movement reported on the especially controversial of imposing a cap on Medicaid payment to the states.

While House and Senate budget leaders expressed pleasure at progress of the 250-member conference, which has been split into 58 "mini-conferences" meeting all over the Capitol, congressional leaders issued hurry-up orders, warning that a slowdown could delay the Aug. 1 start of Congress' summer recess.

One of the biggest hangups yesterday came over a White House proposal, pushed by Senate Labor and Human Resources Committee Chairman Orrin G. Hatch (R-Utah), to include family-planning funds in a proposed health block grant.

House Democrats, fearing that the program could vanish if forced to compete for funds within a block grant, want to keep is as a seperate entity with a guarantee that money will go to local clinics for family-planning advice and services to women, a cause opposed by many conservatives.

To break the deadlock, Hatch proposed earmarking part of the blcok grant for the next few years for family planning, but Democrats said that wasn't enough.

On food stamps, Senate Agriculture Committe Chairman Jesse Helms (R.-N.C.) pushed for further benefit reductions beyond cuts that already would force about 1 million of the more than 22 million food stamp recipients off the rolls. The conferees broke off without resolving the dispute.

Banking Committee conferees had better results as they reached agreement on housing subsidy cutbacks, paving the way for ratifying their tentative agreement Tuesday to drop a Senate demand for curtailment of housing assistance to cities that practice rent control, among them Washington and New York.

They split their differances on the number of new subsidized housing unit for next year, approving housing units for next year, approving about 153,000, a big cut from the 260,000 units former preisdent Carter proposed. They also approved compromise language that would encourage allotment of new or vacant housing to very poor families.

And, in what amounted to a victory for nature through austerity, the conferees agreed to phase out over two years the program of flood insurance for lunderdeveloped coastal barrier islands, a goal sought by environmentalists to protect the natural state of the islands.

Agreement also was reached on relatively minor differences in child-nutrition and jobs programs, among others. The once-huge public service jobs program already had been killed by the two chambers. But other job-training programs were funded at about $100 million more than had been approved by either house.

Meanwhile, Democrats continued to press their campaign against Reagan's proposed Social Secutiry cutbacks, including elimination of the $122-a-month minimum benefit.

"I think Social Security is the Bert Lance of the Reagan program," said House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), speaking of the political embarrassment the one-time budget director caused Carter. It's an issue, O'Neill added, that "goes nowhere but down."

Senate Minority leader Robert C. Byrd (D.-W.Va.) added to the drumbeat with a letter to Reagan that characterized the proposed cuts as a breach of faith and reiterated the Democrats' position that Social Security's immediate problems could be solved by permitting the retirement fund to borrow from the healthier disability and Medicare funds.

Republicans also continued to show discomfort over the Social Security issue. Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) told reporters that he is confident that President Reagan will "address this issue," meaning the minimum beneifit, in his planned television address on Social Security.

Baker said "virtually everyone" in Congress favors dealing with the problem of elderly poor people who will lose income when the minumum benefit is eliminated, although he said it may be in some form other than restoration of the minimum benefit.