The Senate will begin debate this afternoon on a proposal of Sen. Abraham A. Ribicoff (D-Conn.) to extend special tax credits to parents with children in college.

Defeated by a 10-7 vote in the Senate Finance Committee, the Ribicoff proposal would allow up to $325 a year for each student enrolled in college. Credits would be granted on a sliding scale to cover the actual cost to the parents of tuition, fees, and books.

Debate Agreed To

Despite the Committee decision, the Senate agreed by unanimous consent Friday to debate the bill for no more than five hours today and to vote on the measure Tuesday after a maximum of one hour debate.

The special credit is being offered as an amendment to the Administration's tax bill, which emerged from Sen. Harry Byrd's (D-Va.) Finance Committee last week. It does not appear in the House version of the bill, passed last fall.

Although an interesting collection of senators may finally vote for the bill, strong Administration opposition is expected to defeat it. If passed, the bill would result in a revenue loss of up to $800 million next year and an estimated $1.3 billion by 1970.

The Johnson Administration, which has pledged itself to cut taxes and the existing deficit in the budget, reportedly feels that the Ribicoff proposal would upset its very delicate budget projections.

Fears Budget Upset

Even if the Senate does approve it, the measure faces a bleak future in the House, where it would have to win the approval or at least the consent of Rep. Wilbur D. Mills (D-Ark.). Mills has traditionally opposed similar bills, and the House in general lacks enthusiasm for any fiscal measure initiated in the Senate.

Still, the amendment is not yet dead. Last year, when Sen. Thomas J. Dodd (D-Conn.) and several other senators pushed for a more generous tax credit or some form of tax exemption for college expenses, opponents demanded that any action taken be part of a general tax bill.

Now it is being considered in that light, but the opposition is claiming that insufficient attention has been given to the bill. There have not been any hearings on this particular measure.

In the past there has been some debate about what form any tax relief should take. Dodd proposed an outright exemption of $1200, but Sen. Hubert Humphrey (D-Minn.) has been favoring a tax credit, which permits the parent to deduct a specified amount from his, tax bill. It is argued that credit will be of more assistance to persons of low income than the exemption.

Johnson Favored Guarantees

While a senator, Lyndon Johnson favored still another form of assistance, and this may yet be considered. Johnson, in 1960, put a bill in the Senate hopper asking the Federal government to guarantee private loans taken to finance college costs. Similar to FHA loans in principle, this system would release more private funds for education without significant cost to the government.

Even though the Administration is openly hostile to the Ribicoff amendment, a spokesman for Sen. Humphrey said yesterday that Humphrey, the Senate Assistant Majority Leader, probably would vote for the bill.

Other liberal senators, reasoning as Sen. Eugene McCarthy (D-Minn.) did last year that the advantages of exemptions and credits could be given as profitably to parents as well as to business, may join Ribicoff and Humphrey on Tuesday.

Dirksen Reported Opposed

While Republican leader Sen. Everett Dirksen (R-III.) is reportedly opposed, Republican opposition may not be unanimous. Conservatives, particularly Sens. Barry Goldwater (R-Ariz.) and Peter Dominick (R-Colo.), put similar, though more generous, bills in the hopper last session. These men have claimed tax credit is a "means for encouraging more effort at the private level" and therefore more healthy than direct Federal aid.

The Ribicoff amendment would allow 75 per cent credit on the first $200 of college costs, 25 per cent on the next $300 and 10 per cent on the next $1000, making a maximum exemption of $325 dollars on costs of $1500 or more. Credit would be reduced by $50 for every $5000 of income over $25,000 and would be denied altogether when gross adjusted family income exceeds $57,500. Credits could be claimed for each child in college under the Ribicoff bill.

According to one Senate source, the vote may be close, but Ribicoff is not expected to offer a smaller credit to win additional votes