President Barack Obama’s push for a $9-an-hour minimum wage in his State of the Union address this week has already been rejected by Speaker John A. Boehner, but that’s not necessarily a bad thing for Democrats.

As the president and his fellow Democrats look for popular wedge issues in their effort to hold on to the Senate and their long-shot bid to retake the House in 2014, the debate could prove a useful cudgel regardless of whether the policy becomes law.

The White House is clearly eager for the fight; the administration put out extensive documentation on the minimum wage proposal and contends that it will not harm job creation and will boost the take-home pay for nearly 15 million people.

And Obama reiterated the push to increase the minimum wage Wednesday in a post-State of the Union speech in North Carolina.

“I believe we reward effort and determination with wages that allow working families to raise their kids and get ahead,” he said. “And that’s part of the reason why I said last night that it’s time for an increase in the minimum wage, because if you work full time, you shouldn’t be in poverty.”

Unions and senior Democrats predictably cheered, but Republicans and their allies panned it.

Boehner tried to kill the idea in its crib Wednesday morning.

The Ohio Republican’s message was simple — a higher minimum wage would mean fewer jobs, hurting many of the people it aims to help.

“When you raise the price of employment, guess what happens? You get less of it. At a time when the American people are still asking the question, ‘Where are the jobs?’ why would we want to make it harder for small employers to hire people?” he asked.

Boehner continued, “Listen, I’ve got 11 brothers and sisters on every rung of the economic ladder. I know about this issue as much as anybody in this town. And what happens when you take away the first couple rungs on the economic ladder, you make it harder for people to get on the ladder.”

Boehner said many people are earning minimum wage because they have no skills, and if their jobs go away, it’ll be harder for them to gain skills.

But Democrats and the White House quickly jumped on the comments.

“If the GOP is opposed to raising the minimum wage, what is their plan to ensure people who work full time don’t live in poverty?” Obama senior adviser Dan Pfeiffer tweeted.

“The simple fact is that millions of hardworking American families are being squeezed while they watch Republicans protect tax breaks for CEOs to get even richer,” said Emily Bittner, spokeswoman for the Democratic Congressional Campaign Committee. “In this country, we believe that anyone who works hard shouldn’t also have to struggle to pay their rent, their utilities or their grocery bills — but tea party House Republicans and Speaker Boehner seem to care more about millionaires than hardworking families.”

More broadsides like that one are likely.

Both sides have think tank studies purporting to show minimum wage increases help or hurt the economy; Republican aides showed a graphic correlating the last minimum wage increase with a spike in teen unemployment, and conservative groups and think tanks put out statements describing the policy as a recipe for disaster for workers.

But the issue comes down to fundamentally different views of how government should intervene in the economy — with Obama enacting new health care mandates on businesses and now pushing higher wages, and the GOP arguing that growth will come when the government gets out of the way.

It’s one thing to make that argument in a talk at a conservative think tank, but it’s another to use it to win over public opinion. Republicans believe that they can do that this time around with stats at their back and say they aren’t sweating the issue; Democrats are equally sure that they’ll have public opinion firmly on their side.

The last time the parties tangled over the minimum wage, it ended up as a staple of Democratic messaging heading into the party’s 2006 takeover of Congress.

The fight to increase the $5.15-an-hour minimum wage was used by Democrats to bash Republicans as beholden to the wealthy — especially after then-Senate Majority Leader Bill Frist, R-Tenn., tied an increase to an estate tax cut and refused to decouple the issues.

Democrats, in turn, came out against any increases in congressional pay until the minimum wage went up.

Legislation setting the current $7.25-an-hour wage ended up on a compromise war funding bill signed by President George W. Bush the following year, after Democrats had taken over both chambers.

The issue died down nationally for several years — even though Obama proposed a $9.50-an-hour rate in his 2008 campaign. However, the issue has become a staple of fights in state capitals.

In New Jersey, Gov. Chris Christie recently vetoed an effort to raise that state’s minimum wage to $8.50 an hour and tie future increases to inflation, according to news reports. Christie offered instead a $1 increase to $8.25 over three years. New Jersey Democrats are now looking to put a minimum wage increase on the ballot for voters this fall.

The New Jersey newspaper The Record reported the ballot measure has Republicans worried about spillover effects on other races and the potential for the business community to divert its resources to fighting the referendum.