"The problem is in Washington, they talk past one another and they're so polarized they can't seem to get anything done," the GOP lawmaker said Sunday on NBC's "Meet The Press.
Gov. Steve Beshear, a Democrat from neighboring Kentucky, advised critics need to "take a deep breath."
"It'll take us a while to get it in process," Beshear said, "but I'll guarantee you we're going to make it work because it's good for the American people and it's good for Kentucky."
He said residents "started swarming all over" the state's exchanges when they opened Oct. 1. Beshear said some 300,000 Kentuckians have browsed the site and more than 26,000 had signed up.
"We had and have some of the worst health statistics in the country," he said. "And it's been that way for generations. The only way we're going to get ourselves out of the ditch is some transformational tool. That's what the Affordable Care Act is going to do for us."
Kasich, defending his state's refusal to participate in setting up the exchanges, says the troubled roll-out has "everybody just shaking their heads."
"That's like three things, the government almost shut down; now they're tapping someone's phone; and now this thing," Kasich said. "This is creating an issue of confidence in the minds of American people and doubt among people around the world, which is really serious."
"At the end of the day. I think people need to sit down," Kasich said. "The Obama administration needs to open itself up and figure out how we can get some sort of bipartisan support to move forward."
He added that "the rollout is the least of the problem here" because the law "doesn't get to the nub of the problem, which is higher health care costs that have been out of control."