ST. LOUIS — In an outbreak of class warfare, John McCain and Barack Obama swapped sharply worded charges over tax cuts yesterday, each accusing the other of shortchanging middle-income Americans at a time of economic hardship for millions.

McCain, trailing in the polls, fired the first volley, likening his rival to the socialist leaders of Europe and saying he wanted to "convert the IRS into a giant welfare agency, redistributing massive amounts of wealth at the direction of politicians in Washington."

McCain added, "Raising taxes on some in order to give checks to others is not a tax cut; it's just another government giveaway."

Obama responded a few hours later in an appearance before an enormous crowd on the banks of the Mississippi River, saying his Republican rival "wants to cut taxes for the same people who have already been making out like bandits, in some cases literally."

"John McCain is so out of touch with the struggles you are facing that he must be the first politician in history to call a tax cut for working people 'welfare,' " Obama said.

The exchange unfolded 17 days before an election that is trending Obama's way as he bids to become the nation's first black president.

Obama spent the day in Missouri, a bellwether state that voted for President Bush in 2004. Campaign aides, citing local police, estimated 100,000 people turned out to hear him at the Gateway Arch in St. Louis on a sunny day, and 75,000 others turned out for a speech at dusk across the state in Kansas City.

McCain leveled his most critical rhetoric of the day in a paid weekly radio address, and he campaigned later in North Carolina and Virginia, a pair of traditionally Republican states he is struggling to hold. Aides estimated his North Carolina crowd at 4,000 to 5,000, a number he matched later in the day during an outdoor appearance in Woodbridge, Va.

The differences between the two men on taxes have been present from the early days of the campaign, but lately they have attained greater prominence in the wake of a credit crunch, deep declines in the stock markets and rising joblessness.

McCain wants to retain all of the tax cuts that Bush won from Congress in 2001 and later years, reductions that applied at every level of income. For individuals, he also wants to raise the personal exemption for each dependent from $3,500 to $7,000, and has pledged to phase out the Alternative Minimum Tax, which falls on upper middle-class families.

Obama favors retaining Bush-era cuts except on taxpayers making more than about $250,000, whose taxes would revert to higher levels in effect a few years ago.