The Senate Finance Committee has overshot congressional budget limits by $1.3 billion, and either will have to scrap some tax reductions already passed or cut back on the extra relief it was planning for middle-income taxpayers, its chairman said yesterday.

Sen. Russell R. Long (D-La.) told the committee it was in a "fiscal squeeze" over the tax bill it is considering and would have to take drastic action to stay within the budget limits and still enlarge the House bill's tax cuts for middle-income taxpayers.

While not specifying which other measures the panel might cut back. Long hinted that the extra tax relief for middle-income taxpayers ultimately may depend on what happens to the tuition tax credit bill. The controversial measure, which President Carter has threatened to veto goes to conference tomorrow.

The congressional budget resolution allows for $21.9 billion in total tax cuts for 1979 - $20.3 billion for the major tax-cut bill passed in August by the House and $1.6 billion for a variety of other tax bills, including the tuition tax credit measure.

However, Long disclosed yesterday that in drafting its own version of the tax bill, the committee already has exceeded its limit by $400 million, without having voted the extra relief for middle-income persons. It also is $900 million over target for the series of other bills.

The budget squeeze poses a quandary for the panel, which hopes to finish work on the tax bill today. Long asked Treasury Secretary W. Michael Blumenthal to confer with him on the issue this morning in hopes of working out a solution.

Meanwhile, the committee voted yesterday to liberalize the new "targeted" jobs tax credit the House approved as part of the tax bill and revamped some details of a proposal panel members adopted earlier to increase the "earned income" tax credit for the working poor.

It also voted to add $200 million to federal welfare spending for state social services programs - primarily for child-care aid - raising total spending under that program to $2.9 billion, rather than the $2.7 billion approved earlier by the Senate.

And it agreed that, with some minor exceptions, employes should be able to participate in employer-sponsored education scholarship programs without having to pay taxes on the value of the tuition the company pays, even if the extra schooling is designed to prepare them for a new job.

In addition, the committee approved a series of new proposals to liberalize deductions for deferred profit-sharing plans and qualified retirement plans. And it agreed to require firms that provided medical and accident insurance not to discriminate in favor of executives.

The proposal involving the jobs credit would allow employers larger write-offs than the House provided for keeping low-income or handicapped persons on their payrolls for more than one year. Both the House and Senate versions are designed to encourage new hiring.

The House bill would allow employers to claim a credit of 50 percent of the first year's hiring costs, to a maximum of $6,000 a worker, and 16 2/3 percent of the second year's wage costs. The Senate committee provides for a $3,000 credit the first year. $2,000 the second and $1,500 the third.

The committee's new changes in the "earned income" credit proposal it adopted earlier still would raise the write-off to $600 from the current $400 maximum. But the panel voted to alter both the size of the credit granted each low-income worker and the level at which it is phased out.

In the previous version, the committee had voted to increase the credit from 10 percent of the first $4,000 in earnings to 10 percent of the first $6,000 in earnings, and to phase the of income, rather than the current $4,4000 to $8,000.

Yesterday, however, the panel approved a plan that would provide for a 12 percent tax credit on the first $5,000 in income - for a maximum of $600 - and would be reduced gradually until it phased out completely at $11,000 in earnings. The relief would amount to $1.7 billion, instead of $1.8 billion.

The question of adding more relief for middle-income taxpayers is an important one for the committee. President Carter has complained that the bill passed by the House skews too high a proportion of its tax reductions to high and upper-middle-income taxpayers.