The latest CBS News Battleground Tracker shows Sen. Bernie Sanders, I-Vermont, effectively tied with rival Hillary Clinton in Iowa and ahead in New Hampshire, he's not content to rest on his laurels: Sanders also believes he can win in South Carolina, even though the polls show him well behind there.

The poll shows Sanders and Clinton in a virtual tie in Iowa, with Sanders getting 47 percent to Clinton's 46 percent. In New Hampshire, he's well ahead, netting 57 percent to Clinton's 36 percent. The tables turn in South Carolina, however, where Clinton leads him, 60 percent to 38 percent.

The South Carolina poll "is showing us making huge, huge gains," Sanders said on CBS' "Face the Nation" Sunday. "I feel confident that if we can win here in Iowa, if we can win in New Hampshire and those are going to be tough races, I think we stand an excellent chance to win in South Carolina and in Nevada."

"We have a lot of momentum on the ground. I think we're picking up more and more African-American support. Frankly, I think we can win there," he added.

Iowans will head to the caucuses in a little more than a week. Clinton and Sanders have been campaigning nonstop to woo voters in the remaining days, as has Clinton's husband, former President Bill Clinton. He has suggested that Sanders' support comes from the fact that he's "madder" than Clinton, which feels "authentic."

"I am angry," Sanders said. "The American people are angry." He cited the fact that people are working longer hours for lower wages, students accruing tens of thousands of dollars of debt for a college education, and seniors are getting by minimal amounts of Social Security.

But he is also pushing back against some liberal writers who have suggested his campaign is offering too much with promises of tuition-free public colleges and universities and a single-payer healthcare system.

"I think that's really an unfair criticism," Sanders said. "To say that we should make public colleges and universities tuition-free and do what many other countries around the world already are doing and pay for that on a tax on Wall Street speculation, that's not a radical idea. To say that we should do away with loopholes that allow corporations to put their money in the Cayman Islands, pay nothing in federal income taxes and invest that money in rebuilding our crumbling infrastructure, that is not a utopian, pie-in-the-sky idea."

He argued that America has become "dominated so much by Wall Street and big-money interest" that people have forgotten what is possible.

"Yes, I do believe that the wealthiest people and the largest corporations should finally start paying their fair share of taxes. That's what the American people want, that's not utopia," he said.

Moderator John Dickerson dug into Sanders' positions on guns and healthcare, both of which have come under attack by Clinton. He asked about another liberal Democrat from Vermont who ran for president, Howard Dean, who once said that gun control issues should be left to the states and not part of the Democratic agenda.

"I don't believe that at all," Sanders said, suggesting he might have lost his first statewide election in 1988 because he opposed the sale of military-style assault weapons.

He said he supports President Obama's executive actions unveiled earlier this month aimed at strengthening background checks.

"Our goal as a nation, and I think there's overwhelming support for this, John, is to make sure that guns do not fall into the hands of people who should not have them, people who have criminal backgrounds, people who are mentally ill. The federal government does have a very important role to play," he said.

He also defended his "Medicare-for-all" healthcare plan and addressed one criticism of national healthcare plans in other countries, which is that the waiting time to see a doctor can be very long.

"We have 29 million people without any health insurance, and John, they wait a very long time to get healthcare. Sometimes they don't get it at all," Sanders said.

He also said the U.S. is spending three times as much as the British and 50 percent more than the French on healthcare, and both countries guarantee it to all their citizens.

"In my view, a 'Medicare-for-all' single payer system can guarantee quality healthcare to all of our people and at the same time, save middle-class families thousands of dollars a year," he said.

This article has been updated to reflect the fact that Sanders opposed the sale of military-style assault weapons in 1988. He did not oppose a ban on such sales.