They complain that increasing the federal rate from $7.25 an hour would discourage employers from hiring new workers, hurting the very people Obama aims to help.
Obama pointed out in his State of the Union address Tuesday that 19 states and the District of Columbia already have minimum wages set above the federal rate of $7.25, creating a vast wage disparity across the country.
And 10 of those states make annual cost-of-living adjustments, including Washington state, where workers earn at least $9.19 an hour, the highest minimum in the country.
The plan faces certain hurdles in Congress, as top Republicans, including House Speaker John Boehner, wasted little time dismissing the proposal.
More than 15 million workers earn the national minimum wage, making about $15,080 a year. That's just below the federal poverty threshold of $15,130 for a family of two.
Selling his plan to a crowd in Asheville, N.C., on Wednesday, Obama said it's time to increase the minimum wage "because if you work full time, you shouldn't be in poverty."
Advocates say a minimum wage increase can lead to even broader economic benefits.
"These are workers who are most likely to spend virtually everything they earn, so it just pumps money back into local economies," said Christine Owens, executive director of the National Employment Law Project, a worker advocacy group.
That will trigger spending at small businesses in their communities, stimulating consumer demand and driving economic growth, Owens said.
Economists have long disputed the broader impact of setting a minimum wage. A major 1994 study by labor economists David Card and Alan Krueger found that a rise in New Jersey's minimum wage did not reduce employment levels in the fast-food industry. Krueger now is chairman of the White House Council of Economic Advisers.
Yet that study has come under fire from other economists, who argue that comparing different states over time shows that raising the minimum wage hurts job growth.
Mark Zandi, chief economist at Moody's Analytics, said a higher minimum wage would boost incomes for some poorer workers. But it would also discourage employers from hiring more of them.
"So on net, I am not sure it helps," he said.
William Dunkelberg, chief economist for the National Federation of Independent Business, said the increase would hit businesses hard and only hurt low-wage workers by reducing demand for their services.
"The higher the price of anything, the less that will be taken, and this includes labor," Dunkelberg said. "Raising the cost of labor raises the incentive for employers to find ways to use less labor."
The government first set a minimum wage during the Great Depression in 1938. It has been raised 22 times since then -- the last increase went into effect in 2009 -- but the value has eroded over time due to inflation.
Obama's latest plan would raise the hourly minimum to $9 by 2015 and as well as increase the minimum wage for tipped workers, which has not gone up for more than two decades.
As for states that have already set minimum wages above the federal rate, they range from $7.35 in Missouri to the high of $9.19 in Washington. In 10 of those states -- Arizona, Colorado, Florida, Missouri, Montana, Nevada, Ohio, Oregon, Vermont and Washington -- the minimum wage is automatically adjusted every year to keep pace with the rising cost of living.
Women represent nearly two-thirds of minimum-wage workers, while black and Hispanic workers represent a higher share of the minimum-wage workforce than whites, according to the Economic Policy Institute.
The last federal minimum wage increase was signed into law by President George W. Bush, when it increased from $5.15 to $7.25 in a three-step process between 2007 and 2009.
The last recession began in the middle of that process and took an especially heavy toll on middle-wage positions, which accounted for 60 percent of jobs lost in the crushing downturn. Most of the job growth since the 2010 recovery has been in low-wage jobs. Owens, for one, contends, "There's no compelling case to be made that raising the minimum wage triggered job losses."
Doug Hall, director of the liberal Economic Policy Institute, estimates that raising the minimum wage to $9 would pump $21 billion into the economy and lead to the creation of 120,000 jobs.
But Randel Johnson, vice president at the U.S. Chamber of Commerce for labor issues, said the increase would come "on the backs of employers," who would hire fewer people and cut overtime.
"You don't put new burdens on employers when they are trying to recover in a tough recessionary time," he said.
Johnson also warned against tying wage increases to inflation.
"Employer profits are not magically indexed somehow to always go up," Johnson said. "Congress needs to look at the validity of raising the minimum wage in the context of the economic times in which it's being proposed."
That concern is expected to drive Republican opposition in Congress. Florida Sen. Marco Rubio, who delivered the GOP response to Obama's State of the Union address, said Wednesday that raising the minimum wage is the wrong way to help workers increase wages.
"I don't think a minimum wage works," Rubio said on "CBS This Morning." "I want people to make more than $9 dollars an hour. The problem is you can't mandate that."
Boehner, the House speaker, told reporters Wednesday: "When you raise the price of employment, guess what happens? You get less of it."
The Obama administration points to companies such as Costco, Wal-Mart and Stride Rite that have supported past minimum wage increases. The White House says higher wages help build a strong workforce and lower turnover, improving profitability over the long run.