By 2011, about 21 million taxpayers will feel the bite of a law passed three decades ago to prevent supremely wealthy people from escaping taxation. President Bush's proposed tax cuts would push the number even higher, to 36 million.

Democrats and Republicans agree this poses a looming problem for middle-income taxpayers. But because the alternative minimum tax will affect only an estimated 1.5 million taxpayers this year and the heaviest impact won't come until later, the White House and Congress are putting off a permanent fix that could cost at least $300 billion over 10 years.

The problem "is something that eventually has to be fixed, and we will work with Congress to deal with it in due course," said Mark Weinberger, assistant treasury secretary for tax policy.

The alternative minimum tax is a parallel income tax system enacted in 1969 to limit taxpayers' ability to escape taxation through legal deductions, credits and loopholes. Congress was reacting to highly publicized evidence that 155 high-income people paid no income taxes in 1966 by claiming a series of deductions and credits.

Single people with incomes below $33,750 a year and married couples filing jointly with incomes below $45,000 are generally exempt from the alternative tax. But above those amounts, depending on the size and type of credits and deductions that a taxpayer claims against his regular taxes, it's possible that the alternative tax would apply.

The tax rate begins at 26 percent and rises to 28 percent for incomes above $175,000, but unlike the regular tax, fewer deductions and credits are allowed. That means a taxpayer often winds up with a bigger tax bill if the alternative tax applies.

Because Congress never linked the alternative tax to annual inflation adjustments, if nothing is done, more and more people will find themselves calculating and owing the tax as their incomes rise. And if the regular tax is cut as Bush wants and the alternative tax stays the same, the tax breaks promised for millions of people would be reduced because they would be shifted into the alternative tax system.

"The problem is, if you set about doing tax reductions for individuals by cutting rates, the tax cut is going to be an illusion for some people," said Don Weigandt, vice president at J.P. Morgan Private Bank in Los Angeles.

The Joint Committee on Taxation, which provides Congress with official tax bill estimates, projected that about 21 million taxpayers would pay alternative tax by 2011 under current law. But under the House-passed version of Bush's cut in income tax rates, that number would balloon to 36 million.

The alternative tax would be particularly onerous for people who live in states with high income taxes such as New York and California who now enjoy large state tax deductions, and for large families claiming numerous credits and deductions -- precisely the people tax-cut sponsors say they most want to help.

"At least for the middle-class people and down, you don't want the anomaly of giving a tax decrease on the one hand and a tax increase on the other hand," said Sen. Charles Grassley, R-Iowa, chairman of the Senate Finance Committee.

But in an effort to hold his overall tax cut to $1.6 trillion over 10 years, Bush proposed limited relief from the alternative tax by extending through 2002 a temporary protection for people who claim middle-class credits such as the $500 child tax credit and education credits. The House also has taken only modest steps to alleviate the alternative tax in its version of Bush's plan.

Grassley said Congress could act this year to prevent the income tax cuts from throwing more people into the alternative tax in future, particularly those with incomes of $100,000 or less. That could cost $292 billion, according to official estimates.

But if Democrats and moderate Republicans hold fast on an overall tax cut of less than $1.6 trillion, "it might cause me to change my mind" because there wouldn't be enough money unless other parts of the tax package were dropped or modified, Grassley said.

Congress could also repeal the alternative tax outright, a goal long sought by the Internal Revenue Service because of its sheer complexity. But that would cost even more and could result once again in the problem of some wealthier taxpayers escaping income taxes altogether.

The Bush administration wants to concentrate first on getting Bush's tax cuts passed, Weinberger said.