WASHINGTON — President Barack Obama says raising the minimum wage to $9 an hour and tying future increases to inflation will boost the incomes of millions living in poverty and spur job growth by pouring more money into the economy. But business groups are not so sure.

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.