Without pomp or ceremony, the 57 members of the House Appropriations Committee are scheduled to come to order today and formally begin the process of approving the first two of the 13 annual spending bills that will make up the heart of the federal government's budget for the fiscal year beginning Oct. 1.

More than is usually the case, they will be sailing into uncharted waters. Congressional and administration negotiators appear far apart in their "budget summit" talks and Congress has not completed work on a fiscal 1991 budget outline setting spending limits. Such an outline, known as the budget resolution, has passed the House but not the Senate.

As a result, the appropriators are free to proceed without such limiting instructions.

"It's a little scary," said a budget analyst. "They have nothing to restrain them but their own consciences."

Republicans complain that that is no restraint at all. The House-passed budget outline contains about $16.1 billion in new spending initiatives despite signs of a worsening budget deficit in 1991.

The energy and water appropriation bill that will go to the full committee today reportedly contains big increases over the current year for such items as the Superconducting Super Collider, cleanup of wastes at nuclear weapons plants, and water and university construction projects favored by individual committee members. The other measure the committee is scheduled to act on today provides funding for the State, Justice and Commerce departments.

The two bills are part of the more than $500 billion that the appropriators will parcel out to finance the national defense, foreign aid, delivery of the mail, scientific research, space shots, student loans, veterans' hospitals, highways, mass transit, weather stations -- most of the operations of the federal government except automatic benefit programs such as Medicare and Social Security.

In some ways, the committee enters the 1991 budget fray more powerful than ever. At a time of tight budgets, membership on a key Appropriations subcommittee can keep federal money flowing to a home district or state.

That has always been a coveted assignment, but apparently it is no longer enough to guarantee easy reelection. Rep. John P. Murtha (D-Pa.), the powerful chairman of the defense subcommittee, garnered just over 50 percent of the vote in a recent tough primary. Rep. Sidney Yates (D-Ill.), chairman of the Interior subcommittee, also had a difficult race, as did Rep. Bill Alexander (D-Ark.), a member of three subcommittees.

In its role as the ultimate protector of projects and programs, the House Appropriations Committee is in some ways a throwback to the era of the smoke-filled room. Much of the work of the subcommittees goes on informally and out of sight. Deals are cut in unrecorded conversations between members or staffers, and show up in often impenetrable language in the reports accompanying the legislation.

Many of the House subcommittees also draft their bills behind closed doors. That was the case last week when the subcommittee on energy and water met to draft its 1991 bill. The meeting was called on several hours' notice. Lobbyists and reporters who heard about it waited outside while members and staffs carved up billions of dollars in appropriations. Yesterday, members of the Appropriations subcommittee on veterans affairs, housing and urban development also voted to close their bill drafting session.

Just before that there had been an even more important, but also closed door meeting of "the cardinals," the chairmen of the 13 Appropriations subcommittees. They spent 45 minutes dividing the more than $500 billion pot among their subcommittees. Most of the hard bargaining had been done in advance.

That operating style reflects the political roots of the cardinals in an era when major congressional decisions were routinely made in private by the most senior lawmakers. Committee Chairman Jamie L. Whitten (D-Miss.), who turned 80 in April and is as spry and politically savvy as ever, was elected to Congress in 1941. Yates is 80, as is Rep. William H. Natcher (D-Ky.). Two other cardinals, Rep. William Lehman (D-Fla.), and Rep. Neal Smith (D-Iowa), are in their 70s.

The sense of an old-style Hill operation is also reflected in the overwhelming dominance of men on the committee. There are only three women among the 57 members, and one, Rep. Marcy Kaptur (D-Ohio), was elected just this year.