NEW YORK (CNNMoney.com) -- The first minimum wage increase in 10 years takes effect Tuesday, to $5.85 from $5.15 an hour, with two more steps over the next two years taking base pay for millions of workers to $7.25.

But the increase in the federal minimum wage - signed into law in May after a lengthy battle between Democrats in Congress and President Bush and Senate Republicans - still sparks heated debate.

The Fair Minimum Wage Act of 2007 raises the wage in the 18 states that haven't already boosted their minimum wage. The District of Columbia has also raised its minimum wage.

About 13 million workers, or 10 percent of the nation's work force, will benefit from an increase in the minimum wage, the labor-backed Economic Policy Institute said. Of those 13 million, 5.6 million would be directly affected, while 7.4 million low-wage workers will see the spillover effect on their wages.

Wage-hike advocates hailed the increase.

"Yes, I'm glad it's back up, but it's too late now for all sorts of working poor who couldn't pay the rent, or had to cut back groceries for the kids," said author and labor advocate Thomas Geoghegan. "It's a disgrace that we let the minimum wage drop, in real terms, for so long."

The EPI's Liana Fox conceded that the increase doesn't affect 90 percent of the nation's workers but said it was important because the minimum wage is at a 52-year low when adjusted for inflation.

"It's a basic wage floor," said Fox, who noted that other costs have risen since the federal wage was last increased in 1997. The minimum wage was first enacted in 1938.

Steven Davis, of the Chicago School of Business, who is also a visiting scholar at the right-leaning American Enterprise Institute, said increases in the minimum wage can cause employers to respond by looking to reduce labor costs.

"If you subsidize employers to use low-skill workers, they'll seek to use more," he said.

Davis suggests reducing the payroll tax on earnings for both workers and employers.

The "biggest tax paid by low-wage workers is payroll tax not income," said Davis, who noted that the Earned Income Tax Credit is designed to level the playing field for low-wage workers.

"I view that program as a better way of achieving the goal" of easing the burden on low-wage workers.

Fox, however, said the increase in the minimum wage was necessary. "We know there are situations where the free market failed and the low-wage labor market is one of those situations," she said.

"You may be able to get someone to work for 10 cents an hour, but we've decided as a society that that's not a desirable situation," she said.

Geoghegan is more blunt: A raised minimum wage "means, if people live better, there is less disorder and public-squalor blowback. Instead with the drop [in low-end wages], we had a very slow motion Katrina type disaster, a wreckage that the media can't video so we can see it."