Casting his opposition as “shouting” enemies of the average American worker and minimum wage increases, President Obama suggested on Friday that Republicans were faking an interest in the wellbeing of the middle class – and insisted that a recovering economy vindicated his leadership.

“The new plan is to rebrand themselves as the party of the middle class,” Obama said of Republicans, to cheers from core party faithful at the Democratic National Committee winter meeting in Washington DC. “I’m not making this up … I think their shift of rhetoric is good if it actually leads them to take different actions. If it doesn’t, it’s just spin.”

Two weeks after an unusually strong jobs report, the president mixed his teasing criticism of the GOP message with claims of an expanding economic recovery. The announcement this week by Walmart – the nation’s largest private employer – of a minimum wage hike to $9 per hour for all workers, Obama said, was a sign that his economic policies were working.

“If you want to be the party of higher wages, then come on,” Obama said. “Join the dozens of cities and states, companies like the Gap – now Walmart – raising wages. Not just because it’s the right thing to do, but because it’s good for business.” The president repeated a call on Republicans to use their congressional majorities to pass a new federal minimum wage law.

Real hourly wages climbed at just more than 1% over the last 12 months, more than any other year during the recovery, according to an analysis by the left-leaning Brookings Institution.

The president has made calls for a new federal minimum wage law a centerpiece of his economic pitch, and has taken executive action to raise the minimum wage of federal employees to $10.10 an hour from the current federal minimum of $7.25 an hour. The administration has pointed to the passage of four new state minimum wage laws in last November’s midterm election – in Alaska, Arkansas, Nebraska and South Dakota – as proof of support for a new federal measure.

Even as potential 2016 presidential candidates have been courting the middle class with a new economic message, Republicans in Congress have declined to support such a measure in Congress, saying it would amount to harmful regulation and damage businesses.

Six out of 10 Americans favor raising the minimum wage, “including nearly half who are strongly in favor,” according to an Associated Press-GfK poll released Thursday. Only two in 10 oppose a minimum wage hike.

Indulging his crowd’s audible appetite for a bit of partisan zing, Obama mocked Republican opponents from Senate leader Mitch McConnell to Kentucky senator Rand Paul with the refrain: “You can’t just talk the talk; you’ve gotta walk the walk.”

“Our Republican leader of the Senate… starts looking at the jobs numbers, and says: ‘You know, it’s been better because we just got elected, and people are feeling optimistic’,” said Obama, in reference to remarks by McConnell after the sweeping Republican victory in the midterm elections. “Which, OK … I didn’t know that’s how the economy worked, but, maybe. We’ll just call a couple economists.”

Obama’s poke at Paul ended with an invitation for the senator and prospective presidential candidate to visit the neighborhood in Chicago where the president got a start as a community organizer.

“Rand Paul,” Obama said, to laughter. “No, Rand’s an interesting guy – no, he is! And Rand Paul says the Republican party needs to show up on the south side of Chicago, and shout at the top of their lungs” about middle-class wages.

“That’s a good thing. I was just home on the south side of Chicago yesterday. And I guarantee you that Senator Paul would be welcomed there. We are a friendly community. I mean, it’s a little strange if people show up and just start shouting at the top of their lungs. But we’re friendly, it’s going to be OK.”