President Reagan, greeted by applause, cheers and whistles from members of Congress, returned to the public arena last night with a speech warning the legislators not to stand in the way of his programs.

Looking thinner and speaking a bit more softly than before he was struck by a would-be assassin's bullet on March 30, the president seemed otherwise well-recovered from his would as he told Congress that the American people are running out of patience and that Congress risks their wrath if it fails to enact his proposed federal spending and tax cuts soon.

In an address to a joint session of Congress that was interrupted by applause 12 times, never more warmly than when he challenged the legislators to agree with him that old ways of doing business are no longer acceptable, Reagan mixed conciliatory overtures toward Congress with a warning that the people are on his side.

Using the successful space shuttle flight as his example, Reagan appealed, as he has so often in his political career, to the greatness he finds in Americans.

"We have much greatness before us. We can restore our economic strength and build great opportunities like none we've ever had before," he said.

"The space shuttle did more than prove our technological abilities; it raised our expectations once more; it started us dreaming again. The poet Carl Sandburg wrote, 'The republic is a dream. Nothing happens unless first a dream,'" Reagan said.

Although he continued the conciliatory tone that has marked all his approaches to Congress since his landslide election victory in November, Reagan made his main point simply and forcefully.

He quoted Theodore Roosevelt's observation that the American people are slow to anger, but "when their wrath is once kindled, it burns like a consuming flame."

"Perhaps that kind of wrath will be deserved if our answer to these serious problems is to repeat the mistakes of the past. The old and comfortable way is to shave a little here and add a little there. Well, that's not acceptable any more. I think this great and historic Congress knows that that way is no longer acceptable."

Reagan asked the Congress: "Isn't it time that we tried something new?"

The president timed his address to bring maximum pressure on members of Congress who have doubts about his programs in the week they will cost key votes.

If the immediate reaction to his address and the prolonged ovation that greeted his entry into the House chamber -- closely followed by Jerry Parr, the Secret Service agent who pushed the wounded president into a limousine from the drive to the emergency room less that a month ago -- is an indication, the president's program will fare well.

A beaming Reagan tried "thank you" after "thank you" in vain before the welcoming applause subsided.

Although he laid out a short list of his objections to the alternate budget plan drafted by the Democrats of the House Budget Commttee, the president's most powerful appeals were based on emotion and faith in the American spirit.

"All we need to have is faith, and that dream [that we can do better] will come true. All we need to do is act, and the time for action is now," he said in conclusion.

To the Democrats who have placed a higher priority on balance the budget than on cutting taxes, Reagan said that was an inappropriate choice. The American people, he predicted, will back his package of spending and tax cuts.

Reagan began his first public speech since a bullet pierced his left lung March 30 by denying that the attempt on his life justifies calling the United States a "sick society."

With the optimism that Reagan has brought to every aspect of his political life, he said that the warm response from Americans who have sent him messages of friendship and love have given him and Nancy Reagan "a memory we'll treasure forever."

"And you've provided the answer to those few voices that were raised saying that what happened was evidence that ours is a sick society," he added.

Sick societies don't produce men like the space shuttle pilots or like the Secret Service agent who turned to block with his body a bullet aimed at Reagan, or dedicated men like the police officer and press secretary James S. Brady who also were shot with Reagan, the president told his audience in Congress and on TV.

He quoted a letter from second-grader Peter Sweeney of Rockville Centre, N.Y., who counseled the president: "I hope you get well quick or you might have to make a speech in your pajamas." The president wore a blue suit with a blue-striped tie last night in his theatrical return from convalescence designed to demonstrate that he is fit and fully in command.

Turning to his message that it is essential that Congress approve his program, Reagan said:

"Thanks to some very fine people, my health is much improved. I'd like to be able to say that with regard to the health of our economy."

It has been six months since he defeated President Carter, Reagan reminded Congress. Inflation, mortgage and unemployment rates have not come down. The average worker's hourly earnings are lower than they were six months ago, and more than 6,000 business have failed, the president said.

"Six months is long enough. The American people now want us to act, and not in half measures. They demand, and they have earned, a full and comprehensive effort to clean up our economic mess," Reagan said.

His election victory carried a message, he said.

"That message was very simple. Our government is too big and it spends too much."

The House, Reagan noted, is about to consider two alternate economic measures: one drafted by the House Budget Committee and a substitute introduced by Reps. Phil Gramm (D-Tex.) and Delbert L. Latta (R-Ohio).

"On behalf of the administration, let me say we embrace and fully support that bipartisan substitute," Reagan said of the plan that would alter some of his proposed cuts, but would result in a fiscal 1982 budget deficit $6.1 billion less than the $45 billion Reagan proposed.

The other plan, he added, falls short "of the essential actions we must take."

Reagan cited multi-year totals to indict that plan, shaped under the leadership of Budget Committee Chairman James R. Jones (D-Okla.).

It would permit U.S. spending of $141 billion more through 1984 than the Gramm-Latta bill, Reagan said.

The president also attacked it for cutting more than $14 billion in "essential" defense spending over the same period. It also would sharply increase taxes. "In short, the committee measure reflects an echo of the past rather than a benchmark for the future," Reagan said. The speech was Reagan's third economic message since he became president. "The economic recovery package that I have outlined to you over the past few weeks is, I deeply believe, the only answer we hve left," he said. Tax cuts coupled with spending cuts "will make our economy stronger, and the stronger economy will balance the budget, which we are committed to do by 1984," he said. Americans have always been different, the president added. "We've been courageous and determined, unafraid and hold. Who among us wants to be first to say we no longer have those qualities?"