President Reagan pledged yesterday to do "all I can" to win congressional approval of a resolution for a constitutional amendment to require balanced federal budgets.

Reagan's remarks in a brief speech in the White House Rose Garden came as the Republican-controlled Senate began debate yesterday on the amendment. Rep. Barber B. Conable Jr. (R-N.Y.) also filed a petition to get a bottled-up companion bill discharged from committee and sent to the floor of the Democratic-controlled House.

Presidential aides confirmed yesterday that the White House is working on a plan to have Reagan continue his campaign for the balanced-budget amendment at an unusual rally on the steps of the Capitol Monday.

"We must not, and we will not, permit prospects for lasting economic recovery to be buried beneath an endless tide of red ink," Reagan said in his Rose Garden remarks. "Americans understand that the discipline of a balanced-budget amendment is essential to stop squandering and overtaxing. And they're saying the time to pass the amendment is now."

Asked by reporters why he does not act to balance the budget now, Reagan responded: "Because I think that the built-in spending increase is too much for that. The amendment will speak for itself."

He refused to answer further questions, saying that if he did so, he would not be able to shake the hands of the congressional supporters who had stood with him and Vice President Bush as he spoke.

Aides acknowledged the difficulty of having Reagan campaign for balanced budgets after becoming the first president to submit a budget with a deficit exceeding $100 billion. But, they said, it enables him to talk about future initiatives for economic reform during a congressional election campaign this year, in which the question of whether his own economic recovery program has failed is expected to be a central issue.

One administration insider said Reagan's emphasis on balanced budgets was "an exercise in survival" designed to show that the president remains committed to lowering deficits instead of increasing them.

Long a dream of congressional conservatives, the balanced-budget amendment arrived on the Senate floor yesterday, a year after committee approval, with the endorsement of 61 senators, seven short of the number required for passage.

It is expected to pass the Senate, but its path is more difficult in the House where the Judiciary Committee has refused to vote out a similar measure despite several hearings in the past two years.

Conable, the bill's chief House sponsor, yesterday introduced a petition to discharge it from the committee. That would require 218 votes and sponsors already have 223 supporters committed to the amendment, although some of them may balk at voting to discharge it.

Senate sponsors expect several days of off-and-on debate and are committed to opposing several amendments coming from both sides of the aisle.

Pressure has been building on Congress because of the action of 31 state legislatures in calling for a constitutional convention to pass a similar budget-balancing amendment. But this movement has halted three short of the number needed to call a convention.

Sponsors contend that if Congress doesn't propose the amendment for ratification, the states will, posing the threat of a "runaway" convention over which congressmen would have little control.

"No one wants to face a constitutional convention," said Sen. Orrin G. Hatch (R-Utah), the chief Senate sponsor.

Promoters contend that the amendment would force Congress to either adopt a balanced budget each year or vote specifically to permit deficits, thus bringing into the congressional budget process a new measure of accountability.

Its main feature requires Congress to pass a budget in which appropriations do not exceed revenues or to vote by three-fifths majorities in each House to permit a deficit.

This, the supporters argue, would arrest the tendency of Congress to endorse balanced budgets in principle while violating them in practice and would curtail the influence of special interest groups that are able to obtain funds for their pet programs.

Even with Reagan in the White House, "Congress has demonstrated that it is unable to resist the demands for spending and keep them close to the government's revenues," Conable told the House.

On the Senate floor, Hatch claimed the amendment would overcome the congressional "spending bias" and create a new fiscal environment in which spending would be restrained by the available revenues.

Critics have contended that the amendment would put such tight restraints on budget-making that Congress would be hamstrung in times of recession when deficits may be necessary and desirable.

Hatch rejected that, insisting the amendment was "not an attempt to read a particular economic policy into the Constitution." Congress would still be able to approve deficits, he said, but would be forced to vote for them specifically. That would end the current situation in which congressmen are able to "escape public identification for their policies," he asserted.

Sen. Robert J. Dole (R-Kan.) endorsed the amendment yesterday, claiming it would "restore the proper balance to the way we conduct our fiscal affairs."