Earlier Monday, former Michigan governor John Engler told CNBC that the corporate moves to hike wages show that the market is capable of determining appropriate wages.
"Markets work and there's particularly, I think, today a premium on talent," the president of the Business Roundtable said in a "Squawk Box" interview. "But there is also on the part of companies, I think, a desire to retain their workforce. That was what Aetna said, and Wal-Mart was sort of hinting at the same thing. We want to build our own, grow them and train them."
Wal-Mart announced last week that it would boost pay for a half-million of its employees to $9 an hour by April, $1.75 higher than the national minimum wage. By next February, pay will increase to at least $10 a hour. Last month, Aetna said it would raise base pay to $16 an hour.
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The debate over the minimum wage has been going on since it was instituted in the 1930s, Axelrod noted. It's going to be the main message in the 2016 presidential election, he said.
"Any slogan or any principal that a campaign is boiled down to in 2016 has to be about this issue of wages and the ability to get ahead and respecting that fundamental value," said Axelrod, author of the new book, "Believer: My Forty Years in Politics."
He also thinks 2016 could be the year Hillary Clinton captures the White House. While Obama was the right person for the job when he ran against Clinton, every election cycle is different, Axelrod noted, and is defined by the outgoing president.
For example, Obama wanted to change the establishment and was a good counterpoint to President George W. Bush, he said.
"In 2016 people are going to be looking for someone who can manage Washington and who maybe is a little less nuanced than the president is and in that environment, Hillary I think is a much more appealing candidate than perhaps she was in 2008."
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As for Rudy Giuliani, who recently accused Obama of not loving America, Axelrod said he was just clamoring for attention.
"I would write this more off to Mayor Giuliani's desire to be relevant than anything about the president," he said. "I don't know anyone who is more aware of the greatness of America because [Obama's] lived the American dream."