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WASHINGTON (CNN) -- Vermont Sen. Bernie Sanders is staking out ground to Hillary Clinton's left, but he said Thursday he's also winning over support from Republicans who identify with his impassioned criticism of income inequality.

"You'd be surprised there are more than a few Republicans for Bernie Sanders out there. Don't be surprised if we do well with a number of Republicans," Sanders said on MSNBC's "Morning Joe."

Sanders, a self-proclaimed Democratic socialist, has been plagued by doubts about his general election viability since launching his bid for the Democratic presidential nomination.

But Sanders said his message is resonating with "working-class Republicans" who face the same struggles that his campaign platform is so directly targeting.

"You know Republicans have to send their kids to college. Working-class Republicans can't afford to do that. Working-class Republicans have seen their factories shut down and moved to China. Working-class Republicans are equally disgusted about a campaign finance system which allows billionaires now to buy elections," Sanders said.

Sanders' message of combating greed and recklessness on Wall Street and the strong hold corporations have over the U.S. economy is one that "a lot of Republicans will respond to ... as well," he said.

Still, Sanders did not shy away from the fact that "there are strong differences of opinion" between the deeply progressive senator and GOP voters -- from Sanders' support of a woman's right to have a legal abortion to his support for gay marriage to his views on taxes and spending.

Sanders would raise taxes on the wealthiest Americans if he became president because he says the top 1% need to pay "their fair share."

He would also raise the federal minimum wage and institute what he's called a "massive federal jobs program" to put millions of Americans to work -- a costly investment Sanders insists will pay for itself in the long run.

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