Presidential aide Martin Anderson said yesterday the Reagan administration hopes to propose a tuition tax credit to Congress next year. He also said an offer by the nation's governors to pick up the full cost of public education if the federal government would assume the full cost of welfare would probably find little support in the White House.

Anderson, President Reagan's assistant for policy development, said in addition that if future budget deficits are greater than expected, the administration would seek further spending cuts rather than new taxes to reduce them.

Anderson spoke at a breakfast with reporters.

In a separate interview yesterday, deputy Treasury secretary Richard McNamar was more cautious on tuition credits, saying that "there is a lot of work to do yet" on the subject, and that Attorney General William French Smith "still has reservations" as to whether such credits would be constitutional. Cost is another possible problem, he said. But he added that the idea "is tremendously popular in Congress" and if the administration moves, it would probably be toward the end of the 1982 session when members would benefit most politically from taking a popular action.

The controversial tuition tax credit idea, long favored by many Catholic and private school groups, was endorsed by Reagan during his election campaign. Opponents say credits against tuition in parochial schools would be costly, would weaken the public schools and might violate the First Amendment, which requires separation of church and state.

Aides to Sen. Bob Packwood (R-Ore.), co-sponsor of the leading tuition tax credit bill in Congress, said the current version phases in over three years a $500 annual tax credit for tuition paid to elementary and secondary schools and colleges; its cost in today's dollars when fully phased in would be about $5 billion a year. An earlier version was less generous.

Anderson, discussing the administration's long-term plans for "federalism," which calls for turning more responsibilities over to the states, said the "first priority is the welfare program" and the second is education, but declined to elaborate. However, other White House aides on Wednesday said the administration is considering turning federal-state Aid to Families with Dependent Children into a block grant, limiting federal outlays but giving the states more discretion over program rules.

Anderson said he'd be surprised if the administration gave support to proposals, made at the meeting of the nation's governors this week, that the federal government take over Medicaid and welfare entirely if the states agreed to take over transportation, law enforcement and education.

As federalism proceeds, Anderson said, the administration will consider giving some revenue sources to the states to take care of their new burdens. These might include alcohol and tobacco excise taxes or some earmarked portion of the federal income tax, but no specific proposals are now in hand.