Kasich told ABC News Chief Anchor George Stephanopoulos on "This Week" Sunday that the special congressional election Tuesday in a district that Trump won by double digits is surprisingly close.
"It’s really kind of shocking because this should be just a slam dunk [for Republicans] and it’s not," Kasich said.
He said that in the end he believes Republican candidate Troy Balderson will beat Democrat Danny O'Connor in the House race for Ohio's 12th District. "But it really doesn’t bode well for the Republican Party because this ... shouldn’t even be contested," Kasich said.
"Why is it even close?" Stephanopoulos asked.
"First of all, the chaos that seems to surround Donald Trump has unnerved a lot of people," the Republican governor said. "So suburban women in particular here are the ones that are really turned off. And you add to that the, you know, millennials, you -- you have it very close."
Kasich, who ran against Trump for the 2016 Republican nomination and is a prominent critic of the president, also commented on Trump's holding a rally in Ohio on Friday for Balderson.
Kasich said Balderson told him he hadn't had anything to do with the president's decision to come to Ohio.
"I asked him the other day, 'Why are you bringing Trump in?' He said, 'Well, I don't have anything to do with it," Kasich said. "You know, I think Donald Trump decides where he wants to go and I think they think they're firing up his base" with the Trump rallies.
Stephanopoulos also asked about Trump's tweet this weekend taking a swipe at NBA star and Ohio native LeBron James, saying it is hard to make "LeBron look smart."
The tweet Friday came in response to an interview James conducted with CNN host Don Lemon, a frequent punching bag for the president. James spoke to Lemon from the public school he opened for at-risk kids in Akron, called the I Promise school. Every student receives free tuition, as well as free food, uniforms and free bicycles.
Both James and Lemon are African-American. Asked by Stephanopoulos whether Trump was “playing the race card,” Kasich said, Trump "is a divider" and "the chaos" sparked by the president is why the number of people who belong to the Republican Party has declined.
"Republicans have gone from about 30, 31 percent down to about 25 percent," of the electorate, Kasich said. "The party has shrunk because we don't have this positive growth-oriented opportunity message."
President Trump also said in his tweet “I like Mike!” in an apparent reference to the debate over whether LeBron James is better than NBA legend Michael Jordan.
Kasich said on "This Week," “I ended up doing a tweet about that, not only did I say that LeBron should be praised -- look, he has got $41 million set aside to help kids go to college plus a bunch of other schools -- but I also disagreed with the president because you know what, all around LeBron I think is a little better than M.J.”