Budget director David Stockman said yesterday that people who can work shouldn't be collecting welfare.

Stockman also told his enthusiastic audience at the U.S. Chamber of Commerce that new budget cuts for next year were needed because the Reconciliation Act in the summer "stunned, but did not stop . . . the awful momentum built into this budget."

Unless Congress passes the additional $13 billion of cuts and $3 billion of revenue raisers proposed by the president last week, the Treasury will have to finance $80 billion of new debt in private markets next year, Stockman said.

The budget director, who was given a standing ovation, stressed it was both possible and essential to cut the budget further. If "the whole vast array of entitlements" -- such as food stamps, Aid to Families with Dependent Children, low income energy assistance -- "are examined," he said, "it is clear to me that substantial savings are still possible."

Those savings, to be announced in the next month, likely will include further tightening of the eligibility rules for welfare programs.

Stockman justified new welfare-eligibility limits for the working poor and countered criticism that some policies will encourage such workers to quit jobs rather than lose payments by saying: "I have a very straightforward answer to that: If a person is capable of working today," that person should not be able to claim welfare payments.

Stockman told a group of reporters last week that "we cannot solve that work incentive problem in the welfare system by disregards and offsets . . . without putting half the population" on the system. "I think the way you provide incentives for people who are employable to work is to make them ineligible for welfare."

Yesterday, Stockman said he would "like to refute . . . very strongly" the contention that it will prove impossible for the administration to balance the budget in 1984 if defense spending, Social Security and interest charges are all untouched. The remaining $310 billion to $320 billion of the budget will have to be cut about $42 billion, he said, equivalent to 14 percent.