The ammo this jobs report gives the GOP

Friday's jobs report showing a gain of 252,000 positions and a dip to a 5.6 percent unemployment rate offered up more good news for President Barack Obama, who is wrapping up a weeklong road trip to tout the improving economy and offer up fresh proposals on housing and education in advance of his State of the Union address later this month.

Obama, as I reported Friday at more length in Politico, can rightly take credit for some of the improvement in the economy given his early moves on the auto and Wall Street bailouts, the stimulus and actions to bolster the Federal Reserve and hold the line on even greater spending cuts after Republicans took control of the House in 2010.

Read MoreAmerican workers fed up with stalled wages

But the December jobs report also highlighted continuing lines of attack Republicans will be able to make as they craft economic policy in the new Congress and hit the trail for the 2016 presidential campaign.

The report showed that average hourly earnings decreased by 5 cents to $24.57, following an increase of 6 cents in November. On the year, average hourly earnings have risen just 1.7 percent, barely enough to keep pace with inflation. The encouraging 0.4 percent increase in wages reported in November got revised back down to 0.2 percent.

The long-awaited rise in wages still shows few signs of actually materializing, indicating that slack in the labor market remains despite the drop in the overall unemployment rate close to the level at which the Fed will likely have no choice but to start boosting interest rates.

Worker jobs
Scott Eells | Bloomberg | Getty Images

The labor force participation rate also ticked down to 62.7 percent, the lowest level since the 1970s. That number comes from the volatile household survey so probably does not mean very much on a single-month basis. But the overall trend in participation will be very much a Republican talking point over the next two years.

This was evident in former Florida Gov. Jeb Bush—who as expected is blasting to the front of the GOP pack for 2016—launching his new political action committee, Right to Rise, with a pledge to fight for broader-based economic gains.

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"While the last eight years have been pretty good ones for top earners, they've been a lost decade for the rest of America," the Right to Rise website reads. "We are not leading—at home or abroad."

Bush went on to add on the site that "the income gap is real, but that only conservative principles can solve it by removing the barriers to upward mobility."

Look for Bush and other 2016 candidates as well as Republicans in Congress to push for tax reform and some regulatory relief to try and boost business spending and increase wages. Obama will counter with calls to raise the minimum wage and increase subsidies for community college education, as he planned to propose in Tennessee on Friday.

It's clear the White House realizes that the president's economic legacy now hinges on boosting workers' take-home pay.

"We have made a lot of progress," Labor Secretary Thomas Perez told CNBC on Friday. "The unfinished business is to make sure that the prosperity that we see across America is shared prosperity. And the undeniable unfinished business is to make sure we have steady real wage growth."

There is a very good chance this business will remain unfinished as 2015 rolls along as there are few prospects for major agreement in Washington on how to boost wages in the short term. There is always a chance that the numbers will rise on their own as the economy continues to strengthen. But we have been waiting a long time for that. If they don't, candidates on both sides in 2016 will fight the election out in part on how to address the issue.

Read MoreWelcome to 2015, let the political jockeying earnest

Hillary Clinton, assuming she runs and gets the nomination, will have to come up with economic proposals to spark faster wage gains. And so will Bush or whoever else emerges with the GOP nomination. That would actually be a healthy exercise for American democracy. The U.S. is increasingly the envy of the world, economically. But the puzzle of how to boost middle-class wages and standards of living is a vexing one that deserves a very high-level national debate.

—By Ben White. White is Politico's chief economic correspondent and a CNBC contributor. He also authors the daily tip sheet Politico Morning Money []. Follow him on Twitter @morningmoneyben.