President Reagan launches a tax-simplification campaign this week that could produce the crowning achievement of his second term but poses the biggest challenge yet to his reputation as a premier political salesman.

The selling of the Reagan tax plan has been carefully engineered by the White House to arouse the sympathy and support of middle-income and working-class Americans who resent unfairness in the existing system and who would benefit from lowering individual tax rates.

But the task for Reagan is fraught with potential obstacles, according to his own strategists. The president will sell his plan as "populist," but the version he will unveil Tuesday is considerably more generous to some businesses, many wealthy individuals and the oil and gas industry than the first simplification plan his Treasury proposed late last year. Delay or stalemate in Congress may frustrate his hopes of sweeping change. A divisive fight looms over deductibility of state and local taxes. And a surge of opposition is expected from businesses and individuals shouldering a heavier tax burden.

"The greatest single challenge is to mobilize support that is dormant out there to overcome the special interests," a White House official said. "I know of only one guy in the country who can light the fire."

Reagan will attempt to do that beginning Tuesday with a nationally televised address from the Oval Office. The essence of his proposal is to be lower tax rates in exchange for the elimination of many tax breaks.

In selling his proposal, Reagan intends to emphasize the lower tax bills that would result for millions of taxpayers. Reagan is most enthusiastic about this aspect and views it as an extension of his cherished first-term income tax cuts, officials said.

At the same time, Reagan will explain higher tax bills for some corporations as simply making the system more "fair and equitable," the officials said.

In his weekly radio address yesterday, Reagan said his proposal would "remove the dark cloud of unfairness from our tax system. We're going to overhaul the whole rickety jerry-rigged tax code and come out with a newer, sleeker model that will not only be fairer and simpler but will significantly reduce taxes for the majority of all Americans.

"The American people are always willing, even eager, to do their duty," Reagan said. "But you quite naturally resent it when you see others shirking theirs. It rankles to know that your tax rates are so high because others -- who can afford high-priced lawyers and tax consultants -- are able to manipulate the system to avoid paying their fair share. And it simply adds insult to injury when on top of a large tax bill to the IRS you have to pay a professional to tell you how much you owe."

One Republican strategist planning the White House campaign said, "Reagan has to make this a cosmic issue. He has to sell it on a broad plane and get grass-roots support quickly. He has to get people talking about fairness and simplicity. He can't get into the nickel-and-dime issues."

Another administration official said, "Today, it is not a passable bill on the Hill. It doesn't have the public support, yet. For three months, we have to build up a head of steam . . . to convince people it's in their best interest."

As part of this effort, the White House is going to unusual lengths to mute instant criticism of Reagan's proposal. Officials are withholding all copies of the document until the day after the president's Tuesday address. This will give Reagan's rhetoric a critical head start over the specific complaints that are sure to follow once the document is made public, the officials said. Reagan does not plan to hold a news conference -- where he would certainly be asked about his plan -- until late next month.

The "marketing" of tax simplification, as one official called it, will also include a White House speech Wednesday to a "tax reform coalition" being assembled by Reagan aides, appearances Thursday at Williamsburg, Va., and Oshkosh, Wis., and a Friday address to workers and families at a corporate office park in Pennsylvania.

Some officials are hopeful that tax simplification will put Reagan back on the offensive after weeks of setbacks in Congress and perhaps will become a vehicle for making Republicans the nation's majority party. But, in interviews last week, administration officials acknowledged a number of anxieties.

One is the potential conflict between the "populist" or "Main Street" theme that Reagan will aim at middle- and low-income taxpayers and the concrete provisions of his tax plan.

"This populism is anti-big government, pro-market and pro-fairness," Treasury Secretary James A. Baker III said in a speech last week. "Ronald Reagan built his career on this philosophy; he carried 49 states on it, and he can carry tax reform on it."

But with Reagan advancing a plan that is less "populist" than the one proposed last year by the Treasury Department, critics are likely to be taking jabs at the president's rhetoric. House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) has already charged that Reagan's populist rhetoric has been flawed by concessions to interest groups.

A White House official said Baker decided to make these concessions to industry "up front" rather than later. Baker, he said, was tailoring the proposal for a better reception in Congress, and the president approved. In the case of oil and gas tax breaks, Reagan personally argued that they are needed for national security, to encourage domestic exploration for oil, a second official said.

To avoid comparisons with the first Treasury plan, Reagan will ignore it in his speeches, officials said.

Administration strategists also worry about the calendar. Reagan will be trying to drum up support in June and July, when a vacationing public's attention tends to lag. Reagan will take his own vacation in August and restart the tax-overhaul campaign after Labor Day.

The "ideal scenario" would be for House and Senate action in September and October, one official said. But if tax simplification is bogged down in Congress then, officials worry that it could easily slip to next year, when election campaigns could frustrate Reagan's hopes for sweeping changes.

"This is the longest sale we have ever attempted," said a senior White House official. Sustaining it for several months will be difficult, he added.

Yet another challenge seen by Reagan's strategists is an approaching battle over the proposal to eliminate deductions for state and local income, sales and real-property taxes. This has already generated opposition in high-tax states such as New York and New Jersey -- which are represented by two key congressional backers of tax overhaul, Rep. Jack Kemp (R-N.Y.) and Sen. Bill Bradley (D-N.J.). The Reagan strategists say they fear that a strain on the "tax reform alliance" between these lawmakers and Reagan could damage prospects for passage of any plan.

Kemp complained recently that Reagan's plan would not reduce individual rates enough to compensate people in high-tax states for elimination of the deductions for state and local taxes.

Still another White House concern is the strength of corporations and other "special interests" opposing specific aspects of the tax plan.

Reagan could be "chipped to death" by them, said the senior White House official. Another official said industries losing tax breaks will be lining up to show the Congress the "ghastly consequences" in great detail, while the president "has no real ability to answer industry-specific complaints."

Senior officials say they think they have at least divided the business community and thus averted an immediate negative reaction. One official said organizations representing small businesses, wholesalers, retailers, high-technology firms, corporations with high effective tax rates such as General Motors and IBM, and the "good-government managements" will be "ecstatic" about Reagan's proposal.

But the natural-resource, insurance, timber, banking and other industries will be opposed, he predicted.

Reagan's tax proposal will require him to shift somewhat from past rhetoric. He often said in his 1980 election campaign that "corporations don't pay taxes, people do." He won substantial corporate tax breaks in the 1981 tax bill. He suggested in early 1983 that the corporate income tax be abolished because it is "very hard to justify its existence."

Now, he will take a different tack. He is expected to propose a revised corporate minimum tax and advertise it as a "fairness" provision that would prevent corporations from avoiding taxes.

In this approach, White House officials see political gains. "We get the fairness issue back on our side," said one strategist. "We haven't had it in four years. The Democrats took it away from us."

But the attempt to gain political advantage for the Republican Party poses another danger for the White House. Despite the hopes of many Republican strategists that tax simplification could help make the GOP the majority party, Reagan will avoid any such claims, officials say, because of the realization that tax simplification can only be enacted with Democratic support.