Liberal fire met conservative ice in a House hearing room yesterday, and the result -- for so great is President Reagan's strength on Capitol Hill right now -- was predictable: budget director David Stockman skated easily through the heated attacks of his liberal critics.

With cool, almost icy assurance, Stockman set forth before the House Education and Labor Committee the administration's proposals for cutting back various education, job-training, and school lunch programs. With fiery rhetoric and growls of disappointment, the committee's Democratic liberals (Ky.), Augustus F. Hawkins (Calif.) and Peter A. Peyser (N.Y.) -- blasted back.

The Democrats challenged Stockman's statistics -- "you're in the wonderful world of make-believe," Peyser said -- and almost begged him to come up with a new plan that would, as Hawkins put it, "give us answers we can give to individuals who will be hurt by these cuts."

If Stockman was moved an inch by the pleas and imprecations, it was not evident in his responses. "There is an imperative need, in our judgment, to cut spending," he said, and jobs programs and education grants are prime targets.

The budget director did make one generalized promise that pleased the liberals. He pledged to extend his austerity decrees to the Defense Department, which so far has escaped unscathed in the administration's drive to cut the fiscal 1982 budget proposed by Jimmy Carter.

"Their turn is coming next," Stockman said, adding, "There's so much waste in the Defense Department it's taken us a little longer to figure it out."

The budget director offered no details, however, and after the hearing he said he couldn't begin to speculate about how much defense waste there is our which programs are most wasteful. "We'll get to that one day soon," he told a reporter.

Perkins, the committee chairman, who was an original sponsor of some of the programs Stockman has targeted for extinction, noted sadly after the hearing that the Democratic heat probably had had no impact on the budget director. "If he says he doesn't believe our assumptions, I don't suppose he's going to change his mind."

Stockman's unyielding attitude, Perkins added, stems from the general belief on Capitol Hill that Reagan probably has enough support, even in the Democratically-controlled House, to win approval for his budget with few changes.

The 34-year-old budget director sat placidly at the witness table, shuffling a sheaf of charts and printouts as the volleyed arguments with the Democrats, shifting his field when necessary.

At the start of his presentation, for example, he said the administration plans to stop federal funding for a training program that provides local government jobs for unemployed people. The program doesn't work well, he said, because only a third of its beneficiaries land permanent beneficiaries land permanent jobs.

When Hawkins cited a Carter administration study that said 60 percent of the program's workers land permanent jobs, Stockman quickly changed his agrument. If that many of the trainees will get permanent jobs this year, he said, then fewer people will be hurt when the program is ended.

The heat of Democratic criticism was offset considerably by the warm expressions of respect and support Stockman received from committee Republicans.

"Sometime I'd like to have a private session with you, where you can tell me how I can move from a dancer in the supporting cast to be the star," said Rep. william F. Goodling (R-Pa.). "I also have wanted to be president since I was 12, and you apparently have the recipe."