The Congressional Budget Office yesterday said President Carter's new welfare plan would cost the federal government nearly $10 billion more than the administration's public estimates.

CBO predicted that in fiscal 1982, the first year plan would be fully operative if Congress enacts it early next year, federal cost would rise by $13.7 billion over current projected costs, while state and local government cost would drop $4.26 billion.

The Carter administration predicted federal cost would rise by $2.8 billion, while state and local costs would drop $2.1 billion. Welfare programs now cost the federal government $22.8 billion a year and cost state and local governments $11.9 billion, by budget office figures.

The administration's cost projections are in 1978 dollars, while the budget office's are adjusted for inflation. Therefore, they are not directly comparable.

But a budget office staff member said that if their $12.97 billion estimate were converted to 1978 dollars, it would still be $12.4 billion, more than four times the adminstration's estimate.

Overall, the budget office said, Carter's plan would cost all levels of government $49.44 billion, or $9.78 billion more than all the programs it would replace.

CBO presented its figures to a special House welfare subcommittee on the first day of an anticipated month of difficult debate on the new Carter plan.

Even before staff assistant had gone far in summarizing a three-inch-thick book describing the changes Carter wants to make, Republicans and Democrats were suggesting major alterations.

Rep. William M. Ketchum (R-Calif.) said he believes the adminstration should consolidate all the federal government's job creation programs, instead of setting up another one as Carter's plan proposes.

Rep. William Gradison (R-Ohio) said the subcommittee ought to know what Carter wants to do about Medcaid before it tries to create a new welfare system.

Reps. Fred Richmond (D-N.Y.) and Augustus Hawkins (D-Calif) objected to the Carter proposal of paying only the minimum for the 1.4 million public service jobs, something organized labor has come out against.

"There really is a tremendous objection on the part of a lot of people to pay less than prevailing wages," commented subcommittee Chairman James C. Corman (D-Calif.).

Rep. William Clay (D-Mo.) complained that if the food stamp programs were eliminated, as Carter proposes, and poor people were given cash instead, their rents would rise because public housing rents are geared to income.

Clay and others also objected to the proposed welfare system's providing greatly reduced benefits for the first eight weeks in an effort to induce recipients to actively search for work.

"Isn't there any other approach than to to starve them into taking jobs?" asked Rep. Fortney H. Stark (R-Calif.).

Corman has schedule day-long hearings almost every day from now until Dec. 22 in an effort to outline a bill before the Christmas recess, so that it can be voted on "shortly after returning" in January.

"You seem so determine to get this bill out by Christmas and I'm not sure which Christmas you're talking about" Hawkins said at one point.

" . . .Well, I'm not sure either - Corman replied.

Corman is beginning the hearings not by looking at Carter's bill, but by outlining broad major issues, such as: should a new welfare system include both jobs and each assistance, and should all needy people be eligible to participate.

Corman said in opening statement that he first wants the subcommittee to "arrive at some conceptual decisions" about what a new welfare program ought to do, before debating precisely how to do it.

To help the subcommittee understand what Carter has called "the welfare mess," its members have been invited to see a two-hour television movie titled "Welfare." "It would probably be well worth our time." Corman said.