The tax-simplification proposal that President Reagan unveiled last night as "a revolutionary first for fairness in our future" is seen by its advocates as his best chance to revitalize a second term and is significant in part because it contradicts Reagan's cherished views about the merit of corporate income taxes.

Hours before the president spoke on national television about the need to make corporations pay a fair share of taxes and "free us from the grip of special interests," he told a Cabinet meeting that corporations should pay no taxes, administration officials said.

Reiterating a long-held view, Reagan told the Cabinet that corporations simply pass on taxes to individuals. He said, however, that as long as corporate taxes exist, it is unfair for one corporation, such as General Motors, to pay high taxes, while another firm, such as General Electric, pays none.

The contradiction between Reagan's public message and private view reflects some of the tension inherent in a tax plan that for one of the few times will pit Reagan against significant elements of the business constituency that has consistently supported his major initiatives.

The president, who appeared relaxed as he read his speech from a TelePrompTer, made only a passing reference to corporate tax avoiders during his recitation of what he called "America's Tax Plan," but it must have been a chilling one to those who pay no taxes.

Referring to the "one group of losers in our tax plan -- those individuals and corporations who are not paying their fair share, or, for that matter, any share . . . ," Reagan said they will pay a minimum tax and added, "The free rides are over."

Administration officials, if not Reagan, almost welcome the expected opposition from some major smokestack industries, real estate groups and wealthy individuals with tax shelters. They want Reagan to don the mantle of "populism" and campaign for "fairness," until now the battle cry of the president's opponents.

"When the American people hear that large corporations are not paying any taxes or when they hear that extremely wealthy individuals are paying no taxes because they've legitimately used the tax code and its provisions to avoid paying taxes, they say it's not fair," White House chief of staff Donald T. Regan said in an interview.

"If Ronald Reagan stand for anything, he stands for fairness," Regan said.

The attempt to cast Reagan as the white knight of fairness riding forth to battle selfish special interests comes as his presidency appears to have run out of steam. Polls show that Reagan retains the support of a majority of Americans but that his margin of support has dropped steadily since the high point he reached on his second inauguration.

In recent weeks, Reagan has been forced to compromise on several budget and defense issues. He was embarrassed by the controversy over his visit to a German military cemetery.

And the promise of an early summit meeting with new Soviet leader Mikhail Gorbachev appears to have diminished in recent weeks.

As a result, the plan, which Reagan said would lift America "into a future of unlimited promise," comes not when he is at the peak of political strength but when he urgently needs an initiative to recapture the momentum of his presidency.

His aides and intimates say they think that the tax plan could be the make-or-break issue of Reagan's second term.

In discussing the proposal, Regan and presidential intimate Sen. Paul Laxalt (R-Nev.) used the word "hallmark" to describe the proposal. But Laxalt characteristically added words of caution.

"It could be the hallmark of his second term, along with with arms control, but it also has the potential for great mischief," said Laxalt, who shares some conservatives' concern that Reagan's purpose could be undermined if Congress approves a version that goes far in restricting economic incentives.

The nightmare in the White House, where the bill is known alternatively as "Reagan One" or "Treasury Two," to distinguish it from the more far-reaching "Treasury One" proposal of last November, is that the proposal outlined last night will be nibbled to death by amendments from every direction in Congress.

"I've heard estimates of 400 to 500 witnesses on either side," Laxalt said. "We had a monumental hassle on a five-cent gasoline tax last December. When you open up the whole code, lobbyists from all over the country and perhaps the world will be crawling out from any rock."

To avoid losing the tax bill by attrition, the administration will try to insist on the sanctity of the entire package presented last night. The president can prevail if he approaches the issue on "a grand bipartisan scale," according to Kenneth Duberstein, White House director of congressional relations in Reagan's first term.

This bipartisan approach has touched off conflicts between administration strategists who see the tax plan as a Republican issue for 1986 and those who favor a "good governnment" approach that will earn Reagan a historical reputation as a tax reformer but enable Democrats to share the credit.

"It can't be a Republican Party tax bill," a Republican close to the administration said. "You can't win with Republicans and 'Boll Weevil' Democrats as we did in 1981. It's got to be like the tax reform bill of 1982 that was a bipartisan package."

Reagan, who has been bouncing from issue to issue, now intends to follow the communications strategy that has worked best for him -- taking a single issue with broad impact and hammering at it day after day. He will make at least six speeches this week and push the issue hard into July, Regan said.

The White House expects that the issue will then fade from public view and become the focus of attention again when Congress reconvenes in September. Administration strategists hope for a vote in October.

As governor of California, Reagan surprised his critics by making welfare reform -- an issue that many thought incapable of political resolution -- the centerpiece of a successful second term. After years of denouncing the welfare system, much as he has the corporate tax, he decided to embrace and improve it.

But Reagan has rarely criticized corporations, even though some supporters have wanted him to do so.

Last night, Reagan's rhetoric about "corporations that do not pay their fair share" was heavily muted. Considering his long opposition to corporate taxes, the surprise may be that he that he made any critical reference at all.