House and Senate conferees wrapped up about $35 billion in domestic spending cuts for next year last night, and Senate Majority Leader Howard H. Baker Jr. (R-Tenn.) called President Reagan to say he expects the massive bill to be passed by Congress and sent to him by the weekend.

"The bill is done," an aide quoted Baker as saying, even as some conferees were still attempting to tie up loose ends. Negotiators on unemployment insurance went home shortly before midnight, and planned to finish this morning.

Congressional budget leaders estimated that the total saving from the package will amount to roughly $35 billion, which is what Congress instructed its committees to save in spending-cut orders two months ago. In separate bills, the House had approved savings totaling $37.3 billion, and the Senate $38.1 billion, leaving room for slippage in conference.

The break in the budget reconciliation logjam came late yesterday when conferees rejected Reagan's proposed "cap" on growth of Medicaid spending in favor of a reduction in projected costs starting with 3 percent next year, 4 percent in 1983 and 4.5 percent in 1984. The compromise was estimated to save about $1 billion a year.

Another major hurdle had been cleared earlier in the day when conferees reached a health block grant compromise that leaves family planning as a separate program and provides funds to promote teen-age chastity.

As the evening wore on, with conferees shuttling between rooms off the Senate floor, bargainers resolved low-income fuel assistance at $1.87 billion, roughly the current spending level and more than Reagan wanted. A proposal to restrict benefits under the Federal Employes Compensation Act was dropped.

Harried conferees were uprooted by rollcalls on House and Senate floors, and were even displaced by an early evening party as they fought to keep a schedule that would have the bill on Reagan's desk by this weekend.

Resolution of the health block grant controversy was among the most difficult in the three-week conference, both because of the sensitive nature of the programs and because of reluctance on the part of Senate Human Resources Committee Chairman Orrin G. hAtch (R-Utah) to compromise without having the White House fully behind him.

Other increasingly impatient conferees breathed a collectivwe sigh of relief when word spread that Hatch was getting a letter from spread that Hatch was getting a letter from Reagan which, in effect, gave the green light for excluding $130 million in family-planning funds from the health block grants.

Denying that he had been seeking political absolution for preserving family planning, which many New Right conservatives oppose, Hatch said he only told the White House that I think it's time for you guys to stand up and share the burden."

Hatch described the White House letter as saying that "all things considered, they prefer we go ahead with our compromise," even though it fell short of what the administration wanted.

The conferees' compromise combines 20 of 26 health programs into three block grants to the states, cutting spending in the process by 25 percent, or nearly $1 billion, over three years.

"We got 90 percent of what we wanted, considering where we started," said Hatch, in an apparent reference to the fact that the House had proposed keeping most programs out of block grants, where many program advocates fear they will die from lack of interest by the states.

For some programs, such as mental health and alcohol and drug abuse control, states must spend their federal funds as before, although they can sart shifting some in future years. Community health centers will be maintained in a separte block grant. Among other programs kept separate are family planning, child immunization and health services for migrants.

In a bow to conservatives, the conferees agreed to enlarge the existing adolescent pregnancy program to include up to $16.6 million for research and counseling to deter sexual promiscuity among adolescents, including what skeptics called "store-front chastity centers."

An aide to Sen. Jereiah Denton (R-Ala.), who promoted the program, called it "outreach to teen-agers to tell them it's okay to say 'no.'" Denton said: "We're now teaching them to say 'yes' with federal money," an apparent reference to the family-planning program.

But Rep. Toby Moffett (D-Conn.) saw it another way: "We'll be laughed out of every junior high school in America."

In a non-budgetary aside, the compromise also waives the age limit of 64 for the office of surgeon general, which could pave the way for Reagan to nominate his reported choice, C. Everett Koop, an abortion foe, to the post. The agreement requires that the surgeon general have public health experience, but leave the determination of adequate experience to the president and to the Senate in confirmation hearings.

Another knotty issue was resolved when the conferees approved a procedure for the sale of Conrail, the money-losing subsidized frieght railway system for the Northeast, that could keep Conrail operating under government susidies through September, 1984.

The administration wanted to sell it off more quickly. The slower pace is a victory for the House, which wanted to provide more time to sell it as an entity in hopes of preserving service in the region.

Completion of the conference is coming less than five months after reagan challenged Congress to start cutting programs instead of expanding them. Almost all the cuts Reagan proposed were in domestic programs.

They were partly offset by proposed increases in defense spending, with the result the total spending continued to grow under the Reagan projections, though at a much slower rate than before.

With only a few gulps and sputters, Congress swallowed almost the whole thing, leaving relatively few differences to be resolved in conference.

The conference nevertheless was a spectacular affair: more than 250 conferees meeting in 58 separate mini-conferences.