A White House task force is quietly directing a nationwide campaign to defeat California Gov. Edmund G. (Jerry) Brown Jr.'s drive for a constitutional convention to draw an amendment requiring a balanced federal budget, it has been learned.

The unit's strategy, outlined in a 26-page confidential memo to President Carter, also is aimed at thwarting Brown's presidential plans. Brown, who has staked much of his credibility as a national figure on the convention movement, is expected to challenge Carter for the Democratic nomination in 1980.

Actively committing the White House to oppose the convention movement represents a substantial political risk for the president. If he succeeds, Carter could derail a rival who beat him in five 1976 presidential primaries. If the White House loses however, Brown's triumph will be all the greater because Carter had committed his prestige to stopping it.

Twenty-eight of the 34 states required to convene a convention already have passed resolutions calling for such action. Indiana and Montana are expected to follow suit soon.

However, the White House believes its efforts have helped blunt the drive and that it has a good chance of persuading the remaining states to reject resolutions calling for the convention.

"Six weeks ago, it was virtually certain that there would be enough states passing resolutions to call for the convention," said Richard Moe, head of the eight-member task force. "It's still a very close thing, but the odds are close to even that it can be stopped."

Moe, Vice President Mondale's chief of staff, said legislative leaders of the remaining states have been contacted by the White House "and most of them oppose it."

Carter has already spoken out against a constitutional convention, calling it an "extremely dangerous" idea, in answering a question at a press conference on Jan. 17. At a subsequent press conference, he said it would be "very ill-advised, contrary to the best interests of our country."

But the president carefully weighed the political risks of organizing a campaign against the convention movement before he authorized the task force to proceed.

"Many states passed resolutions as a pro forma thing, with no debate or hearings," an administration source said. "But the remaining states are now focusing on the merits of the issues and holding hearings and taking it seriously. We think the more exposure it gets now, the more opposition there will be."

The task force, following strategy outlined in a Feb. 17 memo from the White House senior staff and approved by Carter, has marshaled leproved by Carter, has marshaled legal, economic and politicial arguments against both a constitutional convention and a budget-balancing amendment.

Coordinating its efforts with sympathetic members of Congress, including Sepaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), the unit has recruited governors, other state officials and outside interest groups to oppose the convention movement.

Yesterday, O'Neill's son, Massachusetts Lt. Gov. Tom O'Neill, announced nounced creation here of a group creation here of a group called Citizens for the Coustitution to lobby against the amendment drive in key states. The group was formed with the advice and encouragement of the task force.

Representatives of about 30 different organizations, including a number of labor unions, attended the first meeting. Tom O'Neill said the coalition would oppose the proposal for a convention and initiation by Congress of an amendment of require a ballanced budget.

Moe said O'Nill's group would take over the lobbying activities of the task force, although the White House unit would continue to operate on an ad hoc basis. Other members of the task force are John White, deputy director of the Office of Management and Budget, and White House staffers Tim Kraft, Anne Wexler, Greg Schneiders, Lee Francis, David Rubenstein and Doug Huron.

Despite the task force's efforts, George Snyder of the National Taxpayers Union, the major organization behind the balanced budget amendment drive, said he had not detected any signs of intensified opposition in key states.

"We're right on target," said Snyder, who claimed that the drive would get the support of the necessary 34 states "before the end of the year."

Carter, giving the task force what Moe described as a "firm mandate," agreed on the strategy to oppose vigorously both the constitutional convention and the amendment.

The staff said a convention would be a "nightmare" and would cause a constitutional crisis, pitting the states against the Congress and perhaps against the judiciary. A balanced budget amendment, it added, "presents serious dangers to our economic, social and political system."

The White House has been acutely concerned about the convention movement and its potential for projecting Brown as a national leader since the governor proposed a convention and a bidget-balancing amendment in his Jan. 8 inaugural address.

Nine days later, at the request of Kraft, a Carter political aide, Laurence H. Tribe, a Harvard University law professor, sent the White House a 23-page memo outling legal and political arguments against a convention.

In a summary, Tribe argued that holding a convention under Article 4 of the Constitution would be "unwise for at least two" reasons.

Tribe warned, however, that there were political risks in actively opposing the convention campaign because of widespread public support for a balanced federal budget and limited federal spending. He urged that opposition be coupled with a reaffirmation of commitment to fiscal austerity, a policy Carter has followed.

The call for a convention, Tribe said, "reflects profoundly misguided views of how national fiscal policy should be implemented and how the nation's fundamental law should be amended today."