U.S. military veterans Carlos Villanueva, Hector Villanueva and Pamela Springle, from left, listen as a recruiter for the Internal Revenue Service explains available jobs on Friday in Miami. (Joe Raedle/Getty Images)

A robust economy marked by a boom in jobs and a plunge in gas prices is threatening the longtime Republican strategy of criticizing President Obama for holding back growth and hiring, forcing the GOP to overhaul its messaging at the beginnings of a presidential campaign.

On Friday, the government announced that 257,000 jobs had been created in January and that wages over the past year had increased 2.2 percent. The bump in wages, together with the sharp decline in gas prices, is providing financial relief that could be worth as much as $2,000 a year to an average worker.

The unemployment rate ticked up by one-tenth of a point to 5.7 percent, largely because a wave of people reentered the workforce — or resumed job hunts — after years of discouragement.

“We’re finally getting to that point where a self-sustaining recovery is going on,” said Jeremy Lawson, chief economist at Standard Life Investments, an asset management firm.

The improvement may mark a turning point in the nation’s seven-year-long debate over the state of the economy. Obama came to office amid a financial crisis, promising to turn the economy around. Republicans repeatedly — and, in the 2014 midterm campaign, successfully — argued that he had fallen short, with an economy suffering slow growth and unnecessarily high unemployment.

Marking the 11th month in a row of job gains over the 200,000 mark, American employers added 257,000 jobs in January 2015. The unemployment rate inched up to 5.7 percent. (Reuters)

But a broad consensus among economists that the economy has come to life in recent months appears to be turning that GOP strategy on its head. Some leaders, such as Senate Majority Leader Mitch McConnell of Kentucky, have acknowledged and sought to claim credit for the improvement, which has coincided with Republicans taking control of both houses of Congress.

Other Republicans, while agreeing that the economy is improving, focused on the most glaring problems in the labor market, criticizing Obama for not accomplishing enough.

“We need to build on this recent momentum and continue closing the Obama recovery’s private-sector jobs gap when compared to average recoveries,” Rep. Kevin Brady (R-Tex.), the top House Republican on the Joint Economic Committee, said Friday.

Republican economic strategists say that the economy’s improvement poses a tough challenge for the GOP, potentially undermining the party’s hopes of recapturing the White House in 2016 if they don’t have a message that goes beyond assailing Obama.

“When Hillary Clinton runs, she’s going to say, ‘The Republicans gave us a crappy economy twice, and we fixed it twice. Why would you ever trust them again?’ ” said Kevin Hassett, a former economic adviser to GOP nominees Sen. John McCain (R-Ariz.) and former Massachusetts governor Mitt Romney. “The objective for the people in the Republican Party who want to defeat her is to come up with a story about what’s not great” in this recovery, especially wage growth, he said.

Some in the party have already started to do that, acknowledging the economy’s improvements and tailoring their critiques to an issue more frequently championed by Democrats: the failure of the recovery to adequately boost wages for middle- and low-income workers.

“What you can argue is, yes, right now the economy has the wind at its back,” said Kevin Madden, a former Romney adviser who is a partner at Hamilton Place Strategies in Washington. “Let’s seize this opportunity to deliver broader, sustained growth.”

Former Florida governor Jeb Bush, considered a leading candidate to win the GOP nomination next year, began testing a message this week in Detroit, speaking directly to the struggles and frustrations of the middle class.

McConnell, House Speaker John A. Boehner (R-Ohio) and Rep. Paul Ryan (R-Wis.), the chairman of the House Ways and Means Committee, have all said in television interviews that the recovery is not lifting ordinary Americans in the way that it should.

Meanwhile, Obama said on Friday that the stronger economy is a case for his vision of economic populism.

“My number one priority is making sure the American peoples’ wages and incomes are going up, because right now the stock market has gone up [and] corporate profits are at an all-time high,” Obama said.

“At a time when the economy is finally picking up steam, we’ve got to work twice as hard in Washington,” he said.

The U.S. economy has created more than 1 million jobs over the past three months, the best stretch of hiring in 17 years. That job growth, along with improved consumer confidence and spending, suggests the recovery has finally found a higher gear, more than five years after the Great Recession officially ended.

Most economists expect that 2015 will be the best year for American workers since the recession. Less important than the pace of hiring is the emergence of solid wage growth, an indicator of full labor market health that comes when employers feel pressured to fight for workers.

The average hourly worker saw a 12-cent-per-hour raise in January, the best one-month increase since 2007. Since the Great Recession, real wages have remained stagnant, but this is slowly beginning to change. Over the past year, wages have risen 2.2 percent. Meantime, consumer prices are seeing inflation below 1 percent, because cheaper oil has caused gasoline prices to plummet.

“The pickup in average hourly earnings gains was a belated Christmas present,” Scott Anderson, chief economist at Bank of the West, said in an e-mail. “It should help the Fed look past a temporary drop in inflation this year and keep their eye on gradually normalizing interest rates.”

The typical 40-hour-per-week American worker, according to government data, makes about $1,100 more than he did one year ago. Meantime, savings from gasoline could prove just as important. The typical American spent some $2,400 at the pump in 2013, when prices averaged $3.44 per gallon, according to a government survey of consumers. If gas prices hold steady at the current $2.01, Americans will save $1,000 for the year.

It remains unclear how long gasoline prices will stay low — oil has rallied slightly over the past week — but they’ve already helped drive a psychological change in the way Americans view the economy. Consumer confidence is at a post-recession high, and in January, a wave of people reentered the job hunt after months or years on the sideline. As a result, January’s data showed at least some evidence that these workers are again looking for work. The labor force participation rate — which tracks the proportion of Americans holding or seeking a job — nudged up from 62.7 to 62.9 percent.

“When I look at this report, I see a confident economy,” Department of Labor Secretary Thomas E. Perez said Friday in an interview. “Companies that are bullish. New job seekers who are more optimistic. And when you factor low gas prices and wage growth, that adds up to money in people’s pockets, a greater hop in their step.”

Greg Jaffe in Indianapolis contributed to this report.