Health, Education and Welfare Secretary Joseph A. Califano Jr. yesterday acknowledged that welfare revision may cost more than President Carter has said he wants to spend.

Carter said Monday, in outlining 12 welfare reform goals, that the first should be an initial cost "no higher - than the present system."

"Whether or not that no-higher-initial-cost goal can be met is something we'll find out in the next month or two when we run these computations," Califano told the Senate Finance Subcommittee on Public Assistance.

He said after the hearing that he may give the President two alternatives, listing "this is all we can do for no new money, and for this much more money we can do these other things."

The subcommittee gave Califano a warm and supportive reception, in contrast to criticism directed at him Wednesday by some members of a House welfare subcommittee who were unhappy with delays and the cost ceiling.

Even Sen. Daniel Patrick Moynihan (D-N.Y.), an old social welfare hand who last week attacked as "intellectual bankruptcy" the administration's decision to delay details of its welfare program until early August, had only kind words for Califano.

"This effort that has eluded three Presidents is yours to triumphantly resolve," Subcommittee Chairman Moynihan told Califano as the two hours of testimony drew to a close. "We could not have ended these hearings on a more hopeful note."

Administration sources have said Califano fought hard to avoid the kind of cost ceiling that Carter set.

Others outside the administration, including members of Congress, have expressed doubt that Carter's cost goal can be met, unless the President compromises some of his campaign promises, like federal takeover of local welfare costs.

I want you to take a message back to the head of OMB (Office of Management and Buddget), headed by Bert Lance)," Moynihan told Califano. "He has sent you up here to make brbicks without straw, and it's not easy to do."

Sen. Russell B. Long (D-La.). author of a welfare bill in 1972 which he called "workfare," urged Califano to commit himself strongly to a federal takeover of local government welfare costs.

Although the Democratic Party platform calls for an "immediate" lifting of that burden, Carter's 12 goals issued Monday called for lifting it "as rapidly as federal resources permit."

"I do not know where we will end up on this question," Califano said.