The House and Senate Agriculture committees are expected to finish work this week on food-stamp legislation with only one major question remaining: how deeply they will cut the program.

Both committees appear to be headed toward giving the Reagan administration most of what it wants, meaning that at least 1 million recipients would be cut from the rolls and benefits of about 20 million others scaled down.

The House committee may begin final drafting as early as today, as it continues work on its 1981 farm bill. Its food-stamp subcommittee has adopted a bill cutting the program by $1.3 billion -- close to the administration's target and more than the $1 billion recommended by the House Budget Committee.

Deeper cuts, beyond the $1.3 billion, are anticipated when the full Agriculture Committee takes up the measure.

The subcommittee accepted five of seven major program changes proposed by President Reagan, modified a sixth and rejected only his plan to reduce stamps for families whose children receive free school lunches.

Chairman Frederick W. Richmond (D-N.Y.), although critical of the administration's heavy cuts, said his panel's work "will preserve the basic elements of this program for the nation's needy."

Among other groups opposing major changes, the National Governors Association has alerted its members to resist amendments that would shift new fiscal burdens to the states, which could be on result of the House-Reagan approach.

The picture is less clear in the Senate, where the committee is considering a range of proposals. The mildest, by Sen. Walter (Dee) Huddleston (K-Ky.), would trim he program by about $500 million; the toughest, by Chairman Jesse Helms (R-N.C.) goes well beyond Reagan.

The Helms bill, according to a Congressional Budget Office study, would reduce benefits by more than $4.9 billion a year -- a 40 percent slash -- and remove at least 4 million recipients from the rolls.

An analysis by the Project on Food Assistance and Poverty, describes the bill as "one of the harshest . . . ever introduced during the program's history."

The analysis, written by former federal food-stamp administrator Robert Greenstein, says the Helms bill would most severely affect the elderly and women with young children.

Unlike the other major pending bills, the Helms approach includes resurrection of the purchase requirement (eliminated in 1979) and a mandatory "workfare" program, run by the states, under which receipients would have to work without pay to "work off" their stamp benefits.

The CBO estimates that the purchase requirement would have its sharpest impact among the rural poor and would push at least 2 million participants out of the program -- the would have to pay more for stamps than they would get back.

Among other findings in the Greenstein study: and elderly woman with only federal supplemental security income would lose 54 percent of her food stamps; two elderly women living together on $400 a month would lose 70 percent of their stamps; a welfare mother with $4,200 annual income and three small children would lose about $1,000 in food stamps each year.

Workfare, a requirement in the Helms bill, is made optional in the House and Reagan versions.

The Senate committee also will be considering a package by Sens. Bob Dole (R-Kan.) and Patrick J. Leahy (D-Vt.), adhering closely to Reagan's $1.5 billion savings target, while removing the school-lunch offset and the proposal to put a cap on program spending.

Food-stamp benefits for about 22 million people currently are authorized at $9.8 billion, but the administration has agreed to seek an additional $1.7 billion to carry the program at present spending levels through Sept. 30.