The Senate Budget Committee yesterday approved an economic stimulus package totaling $17.2 billion for the next eight months, including provision for a $300 million program to help low and moderate income families who face a possible cut of their fuel supplies.

The overall size of the package is close to the $17.3 billion tax and spending combination approved last week by the House Budget Committee and is larger than the $15.5 billion stimulus proposal endorsed by President Carter.

The President's top budget official said yesterday that Carter "wants to keep the economic stimulus package pretty well within the limits he proposed." Thomas W. (Bert) Lance, director of the Office of Management and Budget, said the administration puts a high priority on keeping the federal deficit for fiscal 1977 (which ends Sept. 30) under $70 billion.

He told a breakfast meeting of reporters that Carter's tax and spending proposals would result in a deficit of $69 or $70 billion.

The House committee said its stimulus package together with some other revisions it made will result in a $70.3 billion deficit, while the Senate Committee estimates an excess of spending over receipts totaling $68.2 billion.

Neither the House or Senate Budget Committee* s makes any judgments on actual spending or taxing legislation.Instead, the budget committees recommend overall spending ceilings and revenue targets.

Once Congress adopts those spending, taxing and deficit goals it must abide by them unless it takes specific action to approve a new budget. Conber which calls for a spending level on $413.1 billion revenues of $362.5 billion and a deficit of $50.6 billion for fiscal 1977.

Both houses now are hard at work to write an emergency new budget - called a third budget resolution - so that tax cuts and spending increases can be done to stimulate the economy.

The House Public Works Committee yesterday approved a bill which would authorize $4 billion for construction projects that sponsors said could quickly produce 600,000 jobs. That is bigger than the $2 billion proposed by the President, but is the level envisioned by the House Budget Committee in its stimulus package.

Most of that $4 billion addition is not expected to be spent by Sept. 30 - the House Budget Committee estimated only $500 million and the Senate committee $400 million - but agencies have the authority to spend it all if they can and to commit it for spending in 1978 if they cannot.

The Senate Public Works Committee has put off consideration of a similar bill for two weeks.

To qualify for funding under the bill, the public works projects - there are applications for 22,000 of them at the Commerce Department - must be ready to be put under construction within 60 days after approval. This provision is designed to meet criticism that public works projects are poor ways to stimulate the economy because they do not get going until the economy is growing again.

The package approved by the Senate Budget Committee yesterday contained provision for $12 billion in tax rebates and cuts, $1.8 billion in other government payouts to Social Security recipients and $3.4 billion in direct spending programs such as public service jobs and public works.

The House panel approved $3.5 billion in direct spending programs and otherwise developed an overall recommendation similar to the Senate committee's.

While the budget committees theoretically deal only in overall totals, much of what they approve ends up as indirect endorsements of particular programs. The package approved yesterday contains provision for a $300 million programs for families hard-hit by the huge increase in fuel bills due to rising prices and severely cold weather.

No detailed legislation has been proposed yet, although the chairman, Sen. Edmund Muskie (D-Me.), said there would be a limit of assistance of $250 - which go to fuel suppliers to prevent needy families from being cut off.

Lance said yesterday morning - before the Senate committee action - that the administration wanted to keep separate from the stimulus proposals any actions deemed necessary to deal with the high fuel costs or other effects of the abnormally cold winter.

That way, Lance said, Carter could make clear that he did not willingly violate his $70 billion deficit ceiling.

The Senate committee action yesterday proposes a new budget with total spending in fiscal 1977 of $415 billion, revenues of $346.8 billion and a deficit of $68.2 billion. The House proposal last week estimates revenues at $346.3 billion and spending at $416.6 for a deficit of $70.3 billion.