Until Aug. 23, America's major steel companies were virtually unanimous - some vehement - in their opposition to the compromise natural gas legislation that the Carter administration so avidly championed. On Aug. 24 all that changed.

Big steel's flip-flop - brought on by tantalizing hints of federal aid and tax relief - was one modest victory for the White House in its continuing and intense campaign to win the support of key interest groups for the gas ligislation. It is an example of the administration's willingness to engage in old fashioned political dealing even as President Carter defends the gas bill in patriotic terms as a measure of "the national will."

Big steel changed its mind - or at least changed its tune - after a meeting at the White House on Aug. 23 involving senior steel executives, Vice President Mondale, special trade negotiator Robert S. Strauss and Federal Reserve Board Chairman G. William Miller.

That meeting culminated a series of sessions between steel executives and government officials, including officials in the Treasury Department who have been dealing with the steel industry's pleas for tax relief, protection against imports and other aid.

Among those the steel people saw [WORD ILLEGIBLE] Treasury Under Secretary Anthony M. Solomon, author of the "Solomon Report," which outlined feasible federal aid for the industry, and what one steel man called "the trigger price people," who determine minimum prices for imported steel.

"You meet with those people and they say, 'We'll try to be helpful,'" one steel executive recounted, "then you talk to Strauss" about the gas bill. Strauss did not have to draw the connection directly between the two for the steel executives, this company official said. "They're all big boys. They know what they're doing."

"We've got a great deal at stake with the administration," a steel executive said, and Strauss has been "a very active negotiator with the industry" for the administration. "Now he's just going around calling in his checks," this source said.

"If you're going to suck the federal teat, I guess you're going to have to pay for it once in a while," an administration official observed of steel's dealings.

But in fact the steel companies have shifted from what one steel man called "vocal opposition [to the gas bill] to silent opposition," but not to outright support. After the Aug. 23 meeting, steel executives agreed among themselves to put an end to active efforts against the gas bill, but not to hide their true feelings when asked. "We're still against it," one said yesterday. "But only if you ask," said another.

Outwardly, several companies explain their new position in "statesmanlike" terms, as one spokesman put it. In other words, they say they have had to accept the administration's arguments that the national interest could be damaged if the bill is beaten.

But informed industry sources point to bread-and-butter factors that also played a part. Specifically, informed sources said, the industry received administration assurances that the price they will pay for gas under the new bill will not be allowed to rise too far, and that the industry may soon get a tax break allowing for faster depreciation of new plants and equipment.

"I don't know the bucks" involved in the potential tax break, one energy industry lobbyist said yesterday, "but it must be a lot."

A Treasury Department official estimates that the tax change under consideration "could be the equivalent of a 3.3 percent tax grant" or net saving on taxes.

Several oil and gas industry lobbyists working to defeat the gas bill said in interviews this week that the administration strategy is to neutralize big business opposition to the measure, not necessarily to win new support. (However, White House officials claim they do have active support from some key businessmen like Irving Shapiro of DuPont and head of the influential Business Roundtable.)

According to this reasoning, the bill - on which debate may begin today - will be voted up or down by a handful of votes, and the administration will enhance its chances of success if it can minimize the number of business interests actively opposing the legislation.

There have been a number of successful "neutralizations" already. For example, General Motors Corp. has switched from outright opposition to a neutral stance. So have a few textile firms, the B. F. Goodrich Corp., and the National Rural Electric Cooperative Association.

"We're hearing more reports that the president is making headway with the industrial user groups," one gas lobbyist opposing the bill said yesterday.

"The blanket opposition the industrial users were expressing a couple of weeks ago is breaking down a little bit," this source said. "Strauss kept reminding the steel industry how important the position of the government would be. It was the same story with the textile industry. Strauss made it clear that he was about to go to Japan to talk textiles" - that is, restraints on Japanese textile exports to the United States.

Other informed sources said the administration had indicated to industrial users of gas that a provision of existing law allowing them to make special purchases of natural gas direct from suppliers in the intrastate markets in gas-producing states might be allowed to expire if the gas bill is voted down.

These special purchases have become an important source of gas supply for some industries. Schlesinger reportedly raised the issue in a meeting with the Business Roundtable's users' group two weeks ago. According to one source who was present, Schlesinger said the special purchase provision would be in jeopardy" if the gas bill fails.

Some groups, have listened to the administration's pleas and decided not to heed them. For example, an important farm group, the American Farm Bureau Federation, came out against the gas bill despite high-level pressure from the administration.

So has big labor. The president of the AFL-CIO, George Meany, listened to Schlesinger and Labor Secretary Ray Marshall defend the gas legislation yesterday, then decided to write a letter to members of Congress opposing the legislation.

Douglas A. Fraser, president of the United Auto Workers, wrote a letter to all senators yesterday urging them to defeat the gas bill.

Several lobbyists interviewed for this report observed yesterday that White House efforts for the gas bill represented an unusual display of political skill. "I don't fault the administration for dealing," said lobbyist for a consumer-oriented organization. "I wish they'd deal more on some of our issues."

But several Senate aides remarked with surprise yesterday on a duplicated "handwritten" letter their senators had received from Jimmy Carter urging support for the bill.

The three-page letter included a handwritten salutation, signature and postscript from the president, and the body of the message was in his hand, but was obviously reproduced by photocopying equipment or offset printing.

"This is really bush league," one aide to a key Republican senator said yesterday. In another office more sympathetic to Carter, an aide speculated that the White House had not really intended to deceive the senators who got the letter. "It was obviously not handwritten," the aide said.

Opponents of the gas bill yesterday said they were encouraged by assurances that Sen. Russell B. Long (D-La.), chairman of the Senate Finance Committee, had decided to use his considerable talents to work hard against the bill. Interested parties generally agree that Long's role could be key.

Another crucial senator is Howard H. Baker Jr. (R-Tenn.), the minority leader. A source close to Baker said yesterday that the likelihood of his supporting Carter on the gas bill "is diminishing daily."

Senate leaders are expected to decide today, when the vote on the gas bill will come. Sources indicated a vote next week was likely.