President Reagan exhorted a White House-organized rally on the steps of the Capitol yesterday to support a balanced budget constitutional amendment and bring "to heel a federal establishment, which has taken too much power from the states, too much liberty with the Constitution and too much money from the people."

Casting himself in the role of a Washington outsider, Reagan, who has proposed a budget with a record deficit of more than $100 billion, said he was leading a "people's crusade" for the amendment, a mobilization by Main Street "to make government understand its job is to wipe out deficits and not let deficits wipe us out."

Many of the 62 senators and the more than 200 members of the House backing the politically popular balanced budget amendment sat on a platform behind Reagan during his speech. Many confessed privately only a lukewarm enthusiasm for the rally but conceded that the proposed amendment, which appeared dead just a few months ago, is almost sure to pass both houses of Congress.

The amendment is aimed at pressuring members of Congress to be more frugal in budgeting by forcing them to vote in favor of unbalancing the budget when they think it is necessary. The proposed amendment requires a 60 percent majority of both houses for an unbalanced budget.

A lunch hour crowd, which observers estimated at about 5,000, had been given special passes to attend the rally. They gathered underneath a hazy sky in sweltering heat, cheering and applauding Reagan as he spoke from a podium on the West Front steps of the Capitol that was swathed in red, white and blue bunting.

"We don't come as a special interest group pleading for personal gain. We're messengers of a united people demanding constitutional change," Reagan told the flag-waving, cheering throngs which included Capitol Hill aides, members of the Moral Majority, teen-age girls in town for the American Legion Women's Auxiliary Girl's Nation program and federal workers bused to the demonstration.

Ethnic groups, invited to the White House yesterday for Reagan's ceremony proclaiming "Captive Nations Week," were extended "cordial" invitations to attend the rally by presidential assistant Elizabeth Dole.

She told them that there would be iced tea after the ceremony and that they could then receive special VIP tickets and board buses behind the White House for a round-trip to the Hill rally.

As the rally began, volunteers from the Republican National Committee passed out hand-lettered pickets saying "We're for Ron," "Right On, Ron" and "Ron . . . Inflation Down . . . Thanks" which several persons in the crowd later raised and waved as Reagan spoke.

"This is a White House production," said one Senate GOP aide. "At best it's looked on as a Hollywood production."

But he cautioned against downplaying its significance among the general public as a sign of support for budget restraint.

"It's a political thing and it's got a lot of political mileage in it," he said. "Joe Blow out there believes the balanced budget amendment means something."

The amendment has been given new life as the election nears and as attention has been drawn to the presumed effect the federal deficit has had on keeping interest rates high and impeding recovery of the sluggish economy.

Reagan, in his speech, noted that interest on the national debt of more than a trillion dollars is $100 billion and he recalled chidingly how the apostles of the "new economics" had in years past argued that the growing debt was "no problem . . . . We owed it to ourselves.

"So," he said, "we have only balanced the budget once in the last 22 years.

"Runaway government threatens our economic survival, our most cherished institutions and the very preservation of freedom itself," he said.

He did not, however, tackle the irony that as a longtime advocate of balanced budgets, his current budget proposal on Capitol Hill is the most unbalanced in the nation's history.

He again pledged not to defer the third year of his across-the-board cuts in personal income tax as some have suggested to bring deficits down. He did suggest, however, that Congress would have to make "tough choices to control so-called 'uncontrollables.' "

"Uncontrollables" is budget language for government benefit programs whose payments rise with inflation. By far, the largest of those programs is Social Security. Reagan endorsed proposals last year and this year for restructuring or cutting Social Security but backed off both times because of the strong political opposition that ensued.

House Majority Leader James C. Wright Jr. (D-Tex.) denounced the president's appearance as "unabashed show business" and said the reason for the current rash of high deficits "is that Mr. Reagan got exactly what he asked from Congress last year."

Wright and other opponents held a small rally on the Capitol's east grounds shortly after Reagan concluded his speech. About 100 persons showed up.

The congressional opposition is in considerable disarray with no agreed-on tactic for blocking what has taken on the appearance of a budget-balancing juggernaut in recent weeks. House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) indicated last week he thinks the amendment will pass and said he would not try to block its path to the House floor.

However, Wright yesterday seemed ready to question that. He said Democrats are "reassessing" the amendment and indicated that some members may attempt to produce an alternative proposition before the amendment gets to the House.

Other sources said House Democratic leaders have toyed with the idea of proposing a statute requiring balanced budgets to take the place of the constitutional amendment. That would give hard-pressed legislators the election year opportunity of voting for the principle of balanced budgets without having to vote to nail that element into the Constitution. A proposal to do that aleady has been introduced in the Senate by Sen. Charles McC. Mathias (R-Md.).

The constitutional amendment has 62 signed supporters in the Senate, five short of the total needed. In the House, 114 members have signed a petition calling for discharging that amendment from the House Judiciary Committee, where it has been bottled up for months. At least 218 signatures are needed.

That committee's chairman, Rep. Peter W. Rodino Jr. (D-N.J.) has begun an effort to discourage members from signing the discharge petition. In a letter to colleagues, he said the amendment could lead to a "paralysis of government" and would not relieve the financial dilemma.

During several hours of debate in the Senate, critics contended the amendment would have the effect of giving the president vast power to spend money as he sees fit and would give him power to impound funds on grounds that Congress had illegally exceeded spending limits.