WASHINGTON -- House Speaker John Boehner (R-Ohio) only needed a single night's sleep before throwing cold water on one of the most significant proposals put forth by President Barack Obama in his State of the Union address Tuesday night:raising the federal minimum wage to $9 per hour and pegging it to inflation.

"When you raise the price of employment, guess what happens? You get less of it,"Boehner told reporters Wednesday morning. "At a time when Americans are still asking the question, ‘Where are the jobs?’ why would we want to make it harder for small employers to hire people?"

Obama's proposal to raise the minimum wage by $1.75 over the course of three years is hardly radical. The minimum wage, after all, only goes up over time, and even Republican President George W. Bush signed a similarly incremental minimum wage hike into law during his second term.

What probably concerns House Republicans, as well as the business lobby, most about Obama's proposal is not the nominal minimum wage hike. It's the inclusion of a cost-of-living adjustment, which would tweak the minimum wage each year to adjust for inflation. This would guarantee that workers on the lowest rung of the economic ladder don't lose purchasing power, but it would also mean fast-food companies and other low-wage employers would have to pay higher wages just about every year, except in rare cases of deflation.

On Capitol Hill, it means lawmakers wouldn't have to legislate a new minimum wage every few years. The cost-of-living provision would give members of Congress less to squabble about -- and it would basically wipe out a bargaining chip for those who oppose higher minimum wages.

The president's proposal is only a day old, and the battle lines on the issue have barely been drawn. But given the significance of the indexing portion, Republicans may try to give Democrats some kind of nominal increase in the minimum wage while jettisoning the cost-of-living piece of the package. Whether or not Democrats hold strong to the inflation measure may determine if they produce a truly progressive piece of legislation. Without it, the proposal isn't much different from previous minimum wage increases, both Democratic and Republican.

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"Indexing the minimum wage to inflation would help working families make ends meet as costs rise," said Allison Preiss, a spokeswoman for Sen. Tom Harkin (D-Iowa), one of the foremost backers of a higher minimum wage. "Sen. Harkin believes that the ability of these families to afford basic necessities shouldn’t be used as a political football by those in Congress."

Aaron Albright, a spokesman for Rep. George Miller (D-Calif.), said it was critical that the nominal raise and the cost-of-living adjustment come together in a package.

"It is crucial that these two proposals are paired," he said. "It takes the politics out of keeping the minimum wage up with the cost of living, as long as you begin at a fair minimum floor. It gives certainty to working families and businesses."

Jen Kern, minimum wage campaign coordinator at the National Employment Law Project, a worker advocacy group, was more blunt. "Any proposal that doesn't include indexing is a proposal that will erode the minimum wage," she said.

The federal minimum wage has remained at $7.25 per hour since 2009, when the last of a series of increases signed by Bush went into effect. The $7.25 rate translates into a salary of about $14,500, well below a living wage in most areas. The federal rate prevails in 31 states that do not mandate a higher one. Ten states have already put cost-of-living adjustments on their books, meaning minimum-wage workers in those states see a raise just about every year.

A handful of congressional Democrats, led by Harkin and Miller, have pushed for raising the minimum wage in recent sessions. Their bills have gone virtually nowhere, as even many progressives have seemed loath to put much weight behind a minimum wage hike in a down economy. But with the president making just such a proposal on the largest of stages, the legislative environment will now likely change.

On Wednesday, Harkin and Miller announced in a statement that they will roll out a joint legislative proposal to hike the minimum wage higher than Obama has suggested -- to $10.10 per hour -- and raise it with the cost of living. (If the minimum wage had kept pace with inflation since its real-value high in the late 1960s, it would be roughly $10 now.)

Obama once proposed raising the minimum wage to $9.50, back in 2008. Harkin and Miller said the proposal in the president's State of the Union address was "lower than what is needed," though they added that "there is no question that last night he threw the door open for a robust discussion on the importance of raising the minimum wage."

Although indexing is championed mostly by advocates for low-wage workers, the idea has found some conservative adherents as well, given that it provides employers with predictability. Former GOP presidential candidate Mitt Romney, most notably, said on the campaign trail last year that he supported tying the minimum wage to inflation. (He later qualified his remarks, saying the minimum wage shouldn't be raised in a weak economy.) Obama, in his address, jokingly referred to indexing as "an idea that Governor Romney and I actually agreed on last year."

The idea is apparently less popular with House Republicans, however. Rep. Paul Ryan (R-Wis.) was asked by CNN's Jake Tapper after the address if he agreed with his former running-mate on the matter of indexing.

"I have never been a fan of that idea," Ryan responded. "I think it is inflationary. I think it actually is counterproductive in many ways. You end up costing jobs from people who are at the bottom rung of the economic ladder."

"Look," Ryan added, "I wish we could just pass a law saying everybody should make more money without any adverse consequences."

But even given the sluggish economic recovery, Republicans who vehemently oppose the proposal run the risk of looking callous at a time when millions of Americans work but remain poor. After all, minimum wage hikes poll very well with the general public.