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TROY, Mich. — Three weeks ago, Gov. John R. Kasich of Ohio came to Michigan and emphasized the importance of its coming primary. “We have to do really, really well in this state,” he said, “or I have to roll up the carpets and go back.”
But campaigning here in the past week, Mr. Kasich stopped short of describing Tuesday’s contest in such momentous terms. “No, I didn’t say that,” he said on Saturday when a reporter brought up his remark about rolling up the carpets.
Told that he had, in fact, made the remark, Mr. Kasich, who hastened to add that he often spoke off the cuff and without a teleprompter, said he would do well in Michigan, but then turned to the primary that is his main focus these days.
“Do I want to do well in Michigan? Of course I do,” he said. “I’m going to Ohio, O.K.? Let’s not be confused. And I’m going to win Ohio. End of story.”
New poll numbers on Monday suggested he might perform strongly after all.
At the outset in the state, Mr. Kasich’s team went so far as to liken his approach to the way he planted himself in New Hampshire, which rewarded him with a second-place showing.
But in an interview last week with the radio host Hugh Hewitt, Mr. Kasich said there was no circumstance under which he would drop out before Ohio’s primary on March 15. And on Monday, asked whether he had to finish in the top two in Michigan, Mr. Kasich shrugged off the question.
“I don’t feel like I have to do anything other than breathe and take care of my family,” he said. “We’re doing fine.”
He had Michigan to himself for most of Monday, holding two town-hall-style forums in the state before addressing a party dinner here in Troy, north of Detroit.
And a poll released by Monmouth University on Monday found Mr. Kasich gaining ground against Donald J. Trump, though Mr. Trump still had the support of 36 percent of likely Republican primary voters, followed by Senator Ted Cruz of Texas at 23 percent, Mr. Kasich at 21 percent and Senator Marco Rubio of Florida at 13 percent.
“We’re definitely rising in Michigan,” Mr. Kasich told voters in a school gymnasium in Grosse Pointe Woods, a Detroit suburb, on Monday.
He went on to mention that television news programs were saying that Michigan would probably be “very loudly heard” on Tuesday night.
“Please have them say that John Kasich rose,” Mr. Kasich told the crowd, “and his positive campaign is making a difference.”