"The campaigns are spending $4 million of negative ads against me. You think they're worried? They don't spend $4 million ahead of somebody at the bottom," he told CNN's Alisyn Camerota on "New Day."
Donald Trump maintains a wide lead in the Republican primary race in New Hampshire, according to a CNN/WMUR poll
conducted by the University of New Hampshire Survey Center and released Sunday.
Overall, 30% of likely Republican primary voters back Trump, and behind him, the field vying for second includes Texas Sen. Ted Cruz at 12%, Florida Sen. Marco Rubio at 11% and Ohio Gov. John Kasich at 9%.
Cruz tallied a victory in Iowa over rivals Trump and Rubio on Monday night.
But Kasich believes he also can be a roadblock to Trump.
"If I thought he was unstoppable, I'd go back to Ohio tomorrow. He's not unstoppable. It's a long way to the finish line," he said.
Kasich has regularly criticized Trump, calling him divisive and incapable of uniting the country in addressing America's problems.
"The solutions to these problems are not complicated," he said. "The only thing that gets in the way are people who put their party before their country -- people who don't know how to come together or who don't want to come together to let everybody in America have a chance."
Kasich is counting on a strong showing in the New Hampshire primary to spark more interest in his campaign.
"Nobody in the country knows who I am. I'm not a celebrity candidate. I didn't have a national television show. I didn't live in Washington, so nobody knows me," he said.
Kasich said the morning after the New Hampshire primary will be a significant one for his campaign as well as the country.
"We will know on the morning of the 10th whether we are a story. And it's really going to be whether you're saying, 'Oh my goodness, this guy Kasich -- we sort of counted him out,' " he said.
"And then all of a sudden you folks will be forced to shift a little bit of your attention away from the Trumper and you might have to talk about John Kasich," he added.