He made the comments on CNN's "State of the Union" Sunday in response to a videotaped interview with Sen. Ted Cruz, who blamed McCain for the failure of his strategy.
"You know what I think has hurt Republicans? All of the Senate Republicans who have attacked House Republicans," Cruz said in the interview.
But McCain said that although he fought against Obamacare last year and during the election, a government shutdown was not the best way to achieve the goal.
"It was a fool's errand to start with. It was never going to succeed," he said. "This was not an academic exercise, there was damage done to the people of this country."
Although Cruz has said that he is not ruling out a second shutdown, McCain said the American people will not stand for it, and that the Republican party's reputation has already been damaged.
"There are so many things we can do in a positive agenda and get off of this. Keep up the fight against Obamacare, but don't shut down the government and have so much collateral damage," he said.
McCain also called the roll out of the Obamacare website a fiasco, and called for Congressional hearings.
"Send Air Force One out to Silicone Valley, load it up with some smart people, bring them back to Washington, and fix this problem. It's ridiculous. And everybody knows that," he said.