Sanders’s assessment, offered to reporters here after an event at a high school, came shortly after Clinton said on the campaign trail in Iowa that the single-payer health-care plan that Sanders is pushing is a “risky deal” that could be undermined by Republican governors.

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For days before that, Clinton had been aggressively criticizing Sanders on gun control, particularly a 2005 vote to grant legal immunity to gun manufacturers and dealers when their products are used in a crime. Sanders has since said he is open to taking another look at that law, which Clinton opposed while she was a senator representing New York.

Clinton and Sanders were in statistical dead heats in polls of likely voters in Iowa and New Hampshire, the first two nominating states, released Sunday by the Wall Street Journal, NBC News and Marist College.

Previous polls had showed Sanders with a modest lead in New Hampshire and Clinton ahead by a more comfortable margin in Iowa.

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Sanders said Monday that momentum is on his side in Iowa.

“I think the inevitable winner is not quite so inevitable,” he said. “I think we’re going to win this.”

Sanders agreed that he has major differences with Clinton on health care, but he said she was misrepresenting how the kind of plan he is advocating would work.

Sanders supports a move to a single-payer system under which all Americans would be enrolled in Medicare. Earlier Monday, Clinton said she does not want to “rip up” the Affordable Care Act and suggested that Republican governors could undermine the implementation of the plan Sanders is advocating.

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Sanders disputed that, saying: “This is, in fact, a national program, no matter what a Republican governor might want to do.”

On the campaign trail Monday, Clinton said she would continue to talk about the differences she has with Sanders.