The Senate yesterday overwhelmingly approved a revised budget for the current year which makes room for the $13.8 billion in tax relief asked for by President Carter and adds $1.5 billion to the President's spending requests.

By a vote of 72 to 20, the Senate approved a revised fiscal 1977 budget which calls for total spending of $415 billion, revenues of $346.8 billion and a deficit of $68.2 billion, which would be a record.

The House today will take up its revised budget proposal. The House Budget Committee earlier approved a package similar to the Senate's which will add about $1.6 billion to the economic stimulus package proposed by President Carter.

In one of his first moves as President, Carter late last month proposed a package of tax cuts and rebates and new spending designed to stimulate the economy and lessen unemployment.

The Carter program called for $13.8 billion in tax cuts and rebates and $1.7 billion in increased spending during fiscal 1977, which ends Sept. 30. Yesterday, in sending his revisions for fiscal 1978 - originally proposed by former President Ford last month - Carter added another $200 million to his spending programs.

Although the Senate yesterday left room for the tax package proposed by Carter as does the Houses Budget Committee resolution, neither resolution endorses the mechanics of the Carter proposal.

The House ways and Means Committee already has made some major changes in the President's tax plan. The President asked for a $50 rebate for all citizens. The committee eliminated rebates for families which earn more than $30,000. It also scrapped the business tax benefits of the Carter administration and substituted instead, a tax credit up to $1,680 against the wages paid new workers this year and next.

A company could receive no more than $40,000 in such tax credits - 24 new workers - a year. The Ways and Means bill, passed by the committee last week, cuts taxes about $1 billion less than Carter wanted to.

The Senate resolution approved yesterday contains provision for $3.5 billion in spending measures for a stimulus package, compared with the $1.9 billion Carter asked for yesterday. The resolution on the House floor today will provide for $3.6 billion in increased spending.

Rep. Elizabeth Holtzman (D-N.Y.) said she will try to raise that by $200 million to increase revenue-sharing money available to cities hard hit by the expenses of the severe winter. The revised stimulus package Carter sent to Congress yesterday also boosts spending by $200 million for so-called countercyclical revenue sharing.

The budget resolution passed by the Senate yesterday envisions spending $300 million for assistance to families who face having their fuel supplies cut off because they cannot pay gas, oil or electric bills.

Sen. Edmund Muskie (D-Maine), chairman of the Senate Budget Committee, said last week that the administration would not ask for a supplemental bill to provide emergency assistance on fuel bills.

But Muskie aides were hopeful yesterday that the House Appropriations Committee would approve a bill for fuel assistance without an administration request. A Senate source said yesterday that he felt Carter would sign such a bill if it were passed by Congress. The Department of Health, Education and Welfare endorsed the Muskie plan.

The House and Senate are scheduled to iron out the differences between their respective budget resolution next Monday. The budget for fiscal 1977 in effect now - approved by Congress last September - sets a spending ceiling of $413.1 billion, revenues of $362.5 billion and a deficit of $50.6 billion. The budget resolutions which Congress is working on now will supersede last September's budget.