"Now that their grand predictions of doom and gloom and death panels and Armageddon haven't come true. The sky hasn't fallen, chicken little is quiet," Obama said. "The new plan is to re-brand themselves as the party of the middle class. I am not making this up."
To laughs from the Democratic National Committee audience in Washington, D.C., Obama added: "I am encouraged they are speaking about middle class and about wages. But there is this old saying, you can't just talk the talk. ... You've got to walk the walk."
Income inequality and the growing gap between the richest and poorest Americans has become a primary issue in the 2016 election and many Republicans vying for the party's nomination have focused on the issue. The comments have not gone unnoticed by Democrats and the White House.
"We're facing right now a divided America when it comes to the economy," said Sen. Ted Cruz, R-Texas, after Obama's January address to the nation.
"Income inequality has worsened under this administration," Sen. Rand Paul, R-Kentucky, said after the President's State of the Union speech.
On Friday, Obama took on Paul directly, noting that the 2016 hopeful once said his party needs to show up "up on the South Side of Chicago" and shout "at the top of our lungs: 'We are the party of jobs and opportunity.'"
"I think that is encouraging that he wants to go to the South Side of Chicago," Obama said with a smile. "I was just home on the South Side of Chicago yesterday and I guarantee you that Senator Paul would be welcome there. We are a friendly bunch."
Obama added: "I mean, it is a little strange if people show up and just start shouting on the top of their lungs. But we are friendly, it would be OK."
When Obama first mentioned Paul, some in the audience groaned at his name. Hearing this, Obama said, "No, Rand is an interesting guy."
The President views the improving economy after a difficult recession as a potential cornerstone of his legacy. In the foreword to a report on the nation's brightening fiscal picture from the White House Counsel of Economic Advisors, Obama writes "the United States has just concluded a breakthrough year."
Obama has made fewer references to the issue of income inequality in recent months in favor the term "middle class economics," which was a major theme of his State of the Union speech.
Aides to the President insist GOP leaders have flocked to the issue of income inequality only in an attempt to diminish Democratic claims to the nation's improving economy. Before the speech, a White House official said Obama would use his DNC speech to call out Republicans for what he sees as hypocrisy.
"So far, at least, the rhetoric has not matched the reality," Obama said on Friday. "I think the shift in rhetoric that they are engaging in is good, if it actually leads them to take different actions. If it doesn't, then it is just spin."
The President also seemed to lightly touch on recent comments by former New York Mayor Rudy Giuliani, who said earlier this week that he doesn't think President Barack Obama "loves America."
"This is not just a sports contest, this Is not just who's up and down at any given point, it's not about notches on a belt, it's not about ideological battles an proving how smart you are," Obama said. "It's about making this nation we love more perfect."
Republicans, in response to most positive economic numbers, have said there are still glaring vulnerabilities in the nation's recovery.
"After spending the last six years growing Washington instead of the middle class, it's no surprise President Obama can only point fingers rather than point to meaningful success," said Republican National Committee spokesman Michael Short. "The reality is Americans have suffered under the slowest economic recovery in modern times, and on his watch, the middle class lost its status as being the world's richest as more and more families fall out rather than move up."
House Republicans have had a similar response to the President's message.
"There's a reason why the Democratic Party has lost the House, the Senate, governorships, and more than 900 state legislative seats in recent years. President Obama's liberal agenda has left America's working class families behind," Boehner spokesman Cory Fritz said.