President Reagan, elected on the promise to cut taxes, took to the hustings today to sell a $98.9 billion tax increase on the grounds that it wouldn't affect the average American and that much of it is not an increase at all, but the collection of taxes already owed.

Appearing at the centennial celebration of this city by the Yellowstone River, Reagan moved to dispel any uncertainty about his position on the embattled three-year tax increase by describing it as "essential" to trim deficits, bring about economic recovery and preserve last year's personal income tax cuts.

Even as Reagan went public with his appeal for the tax bill -- now in a House-Senate conference committee -- there were hints that he is uneasy in embracing massive deficits and new taxes only a year after he won from Congress the largest tax cut in American history.

"For a conservative president like me to have to put his arms around a multibillion-dollar deficit, it's like holding your nose and embracing a pig," he said. "And, believe me, that budget deficit is as slippery as a greased pig."

The president said $31 billion of the tax boost "isn't a new or added tax in any way," but "the collection of tax now legitimately owed by some citizens . . . which they have not been paying." He added that "about half the total in the bill is correcting unintended tax advantages which have resulted from sloppiness in past legislation.

"One example is a technical flaw in a bill passed several years ago which resulted in some corporations getting a 60 percent tax reduction simply because of that technicality . . . . It was totally uncalled for that they should continue to get that."

Reagan did not identify the "technical flaw."

Sensitive to the election-year politics of the tax bill, Reagan minimized its bite on individual pocketbooks, saying, "Less than one dollar out of five in the bill represents new taxes."

The tax bill would "not raise income taxes on the average American," he added. But he did not mention the doubling of the tax on a pack of cigarettes, from 8 to 16 cents. Nor did he mention increased telephone excise taxes.

"This tax program is part of the entire budget process and was essential in getting support for further reductions in spending," Reagan said. "In order to get $280 billion in reduced outlays over the next three years, we had to agree to the added revenues of $99 billion. The ratio of reduced outlays to revenues is 3 to 1.

"The bottom line is this," he said. "Would you rather reduce deficits and interest rates by raising revenue from those who are not now paying their fair share, or would you rather accept larger budget deficits, higher interest rates and higher unemployment?"

Republican political operatives have said they detect little grass-roots enthusiasm for an election-year tax increase, and that mood was reflected today as Reagan won far more tumultuous applause in recounting his tax-cutting victory last year than for his current tax increase.

The president went beyond his appeal for the tax bill today and delivered a preview of the defense he plans to use in congressional election campaigns this fall against Democratic charges that his economic program has failed.

"Last week, on the anniversary of last year's tax cut vote, there were the predictable partisan cries that the program had failed," Reagan said. "It's only been in operation 10 months . . . . We warned you in the beginning that there would be no instant miracles.

"If I could correct 40 years of fiscal irresponsibility in one year, I'd go back in show business as a magician. You know, that might be more fun pulling rabbits out of a hat than jackasses out of the way in Washington," he said.

"Economic recovery is long, hard work," Reagan said, in marked contrast to his upbeat promises only a year ago that the tax cut would stimulate economic activity quickly. Today, Reagan cautioned that the program would work "slowly and surely."

Later, the president appeared at two fund-raisers for GOP Senate candidate Larry Williams, author of "How to Prosper in the Coming Good Years," who is challenging incumbent Sen. John Melcher (D-Mont.) In the western fashion he knew so well as a Hollywood actor, the president rode around the Metra arena in an old-fashioned stagecoach.

In his remarks today, Reagan read from a letter from a Montana mother of twin sons asking him to "help stop the bomb."

The president pledged to "work hard and unceasingly to protect her sons from nuclear war . . . ." His comments came as a small group of demonstrators outside the Metra arena here carried signs protesting the MX missile. "Bread not Bombs," said one placard.

Montana has 200 silos for Minutemen missiles, and a non-binding nuclear freeze initiative is on the November ballot.