Budget Director David A. Stockman, reversing his earlier position, told Congress yesterday that he and the rest of the administration strongly back a constitutional amendment to balance the budget and limit the growth in taxes.

Such a measure is needed to ensure fiscal discipline, Stockman told a House Judiciary subcommittee, as he expressed "the president's and the administration's support" for the balanced budget-tax limitation amendment now before Congress. He acknowledged that there are problems with such an amendment, which was criticized earlier this month by Federal Reserve Chairman Paul A. Volcker. But Stockman said that those criticisms were not as serious as the present "fundamental problem of fiscal breakdown, of fiscal irresponsibility."

The momentum of spending is "simply so great" under the present budget process that "we need help" in restraining it, he said.

In his confirmation hearings, Stockman had opposed such an amendment, saying that it would not be practical and was not necessary. Yesterday, he commented: "I like to think we keep learning" in life, and said that he had learned that it was harder to control federal spending than he had believed, and that the problems with a balanced budget amendment "are not as serious as I once thought." President Reagan endorsed the idea on public television earlier this month.

Stockman said yesterday that the current budget process would have to be changed if the amendment were approved. He suggested there should be a reserve or contingency fund equivalent to between 5 percent and 8 percent of outlays to make sure that the amendment could be enforced. Under the amendment, Congress would have to approve by the beginning of each fiscal year a statement of revenues and outlays that showed a balanced budget. Actual outlays must then be equal to planned outlays.

Some critics of the amendment have said that the reserve fund would have to be allocated by the president and that this would involve a major shift of power from Congress. In addition, if the reserve were not fully spent, then this could have a depressing effect on the economy, they argue.

Stockman said that one aspect of the amendment should be changed. At present the proposal says a "declaration of war" would allow Congress to waive the amendment's requirements in any year with just a simple majority of votes. This should be changed to allow a "broader range of events--unforeseen events posing an imminent threat to national security--to qualify for a waiver," the budget director said.

There was some skeptical questioning from committee members. Rep. Henry F. Hyde (R-Ill.) called the measure "the ERA for the conservatives," and a "legislative cop-out." Rep. Don Edwards (D-Calif.) suggested that Stockman submit a balanced budget for 1985 or 1986 to the committee so that people could see how this proposal would work. Rep. John F. Seiberling (D-Ohio) asked whether Reagan's tax and spending plan last year could have been approved under this amendment.

Stockman argued that the amendment fulfills three basic criteria that would make it an improvement over the current budget process:

It restrains both deficits and tax growth, by tying revenues to the growth of national income, and requiring that actual outlays should not exceed planned outlays; it is flexible in that it allows Congress to approve a deficit by a three-fifths vote, and a greater increase in revenues by a majority of the full membership; and it is enforceable.