The administration yesterday reaffirmed its support of tuition tax credits for families of private school and college students, but indicated that other education programs may have to be cut to make up the cost, estimated at an initial $2.7 billion a year.

Testifying before a House Education subcommittee, Assistant Treasury Secretary John E. Chapoton said the administration remains committed to the tax credit concept despite its troubles holding down the budget deficit.

However, a League of Women Voters witness warned that the credit would subsidize "segregation academies," and Albert Shanker, president of the American Federation of Teachers, told the panel that the plan would support, with tax dollars, "schools run by cults such as the Moonies or by political extremists such as the Nazis . . . . "

Sen. Orrin G. Hatch (R-Utah), a leading opponent of legalized abortion, introduced a compromise amendment to the Constitution that would give states, as well as Congress, authority to restrict a woman's right to end her pregnancy.

Other recent attempts to outlaw abortion have been faulted as unconstitutional or have failed to muster enough support to win. Hatch's new "federalism" amendment drew fire from both supporters and opponents of abortion rights. It says in part, "A right to abortion is not secured by this Constitution."

"We believe this is the gravest threat to abortion rights since the 1973 Supreme Court decision" that legalized abortion, said Karen Mulhauser, executive director of the National Abortion Rights Action League. Anti-abortion groups oppose it because they want to ban all abortions.

Secret Service agents charged with protecting presidents are frequently overruled by White House aides for publicity-seeking reasons, a former agent and a senator formerly on the Warren Commission told a Senate committee.

The testimony came as the Justice Department endorsed a bill that would make it a federal crime to assault or kill Cabinet members or top presidential aides.

Charles M. Vance, a former agent who married Gerald R. Ford's daughter, Susan, said that agents raising a bona fide security concern should be able to overrule "political, personal and protocol arguments" as to presidential movements. Instead, he said, decisions often were made by some White House staff member interested in "press exposure," "public impact" or a good camera angle.

Sen. Arlen Specter (R-Pa.), who expressed similar sentiments, has introduced a bill to create a presidential protection commission, which might try, among other things, to resolve the continuing conflict between the Secret Service and the White House about how much the president should mingle with the public.

The administration plans to start using photograph identification cards soon to help root out cheaters in the food-stamp program, although it is not known precisely how much fraud exists, witnesses told a House Agriculture subcommittee in a sometimes emotional hearing.

Agriculture Department official John W. Bode said he hoped to institute the cards within a month, and added that the use of electronic funds transfer would do much to eliminate another problem: the theft of food stamps from the mails.

Subcommittee Chairman Frederick W. Richmond (D-N.Y.) said he favors, in addition, "first-endorser liability," meaning that the bank first processing the forms for food stamps would be held responsible for their misuse.

Putting their money where their politics are, two House aides to Rep. Henry J. Hyde (R-Ill.) have pledged to refuse the 4.8 percent pay raise due on Oct. 1, and are circulating a petition inviting their colleagues to do likewise. The sacrifice is designed to express "our confidence in the Reagan administration's economic recovery program," according to the letter, signed by legislative assistants Fran Westner and Nancy Short. The response? So far only "a lot of phone calls, most of them great," said Westner, "but some questioned our sanity or our IQ level."

Confronted with a ticklish issue, regulation of special-interest caucuses, the House Administration Committee yesterday chewed on the bullet in a time-tested fashion and appointed a committee to study the issue.