Sen. Russell B. Long (D.La.) yesterday began pushing a limited national health insurance bill toward the Senate floor. And, to limit its costs, he said doctors should cut their rates for the catastrophically ill.

Saying it is time to act, the Senate finance Committee chairman put his prestige behind an effort to get a health bill through this key committee quickly.

President Carter has proposed a $24.3 billion-a-year health plan. Sen. Edward M. Kennedy (D.Mass.) and labor have a $40 billion plan. In both cases both federal and private funds are counted.

Long's committee instead began work yesterday on what could become a "consensus" bill that is small in scope.

The consensus bill could strongly resemble a $10 billion to $12 billion plan Long is currently describing. Kennedy, almost certainly, and the presedent, perhaps, would then fight on the Senate floor to increase Long's ante.

Finance Committee Democrate and Republicans agreed yesterday that there may be a consensus in the comittee, and in the Senate, for a modestly priced bill.

Most also agreed that, as Long put it, "the most vitally needed protection" is more so-called catastrophic or major medical insurance to cover the big medical and hospital bills that can wipe out families.

Long said last week that he could support a health insurance package costing as much as $20 billion, and would do so, if necessary, to pass a health plan.

But he expected, he said, to seek only a $10 billion to $12 billion package, containing not more than an added $5 billion in catastrophic insurance for the employed and others. Of this $3 billion would be in employer-employe funds and $2 billion in federal money.

Long gave no new figures of his own yesterday, but pushed other members to suggest their ideas. The one with the most visible support behind it, other than Long's was a Dole-Danforth-Domenici bill to spend $6 billion a year - $3 billion federal and $3 billion in employer-employe contributions.

The nation can't even afford Long's $10 billion proposal, let alone Carter's or Kennedy's, Sen. Bob Dote (R.Kan.) said.

But when Sen. Daniel Patrick Moynihan (D.N.Y.) told Dote that more money might be needed to correct the "extraordinary inequalities" of the state-run Medicated Programs for the poor, Dole agreed that his co-sponsors "don't have enough emphasis on the poor and near-poor because of cost." And he indicated a willingness to negotiate.

One of Dole's Finance Committee colleagues, Sen. John C. Danforth (R-Mo.), repeated a past suggestion of his for an added 10-cent-a-pack cigarette tax to raise $3 billion a year to help pay for health insurance. The other sponsor of what members called the "3-D" health bill, Sen. Pete V. Domenici (R.N.M.) wasn't present.

On doctors, and the need to save money in any health plan, Long recalled the old family doctors who "just didn't get paid" sometimes, or took what they could get from the poor "and settled for that."

I think doctors should be willing to take care" of the catastrophically ill today for "less than they would ordinarly charge," which some do any way, Long said.

He suggested that it might be up to the insurance companies handling any new federally mandated insurance to deal with the doctors, as many states do now for Medicaid patients, to set such fees.

Sen. Abraham A. Ribicoff (D.Conn.) immediately pointed out that Long's suggestion that doctors accept lowered, negotiated fees for at least some patients closely resembles Kennedy's plan to negotiate all doctors fees.

There is room for compromise, Ribicoff maintained, not only between Long and the Republicans and the president, but also between them and Kennedy on a health bill.