The 82-year-old actor and director also talked about Oprah Winfrey, Obama's unfulfilled promise to close the U.S. prison at Guantanamo, the wars in Iraq and Afghanistan and lawyers. At one point, he referenced dismissing Obama and making a change.
"When somebody doesn't do the job, you gotta let 'em go," Eastwood said. The tough-guy actor of "Dirty Harry" fame then drew a finger across his throat.
The Obama campaign shot back afterward by tweeting a photo of the back of the president's chair, with Obama's head peeking over it, along with the line: "This seat's taken."
Romney's wife, Ann, said she appreciates Eastwood's support, even if the actor's monologue isn't earning rave reviews. Ann Romney said she did not know what to expect when Eastwood came on as a warm up act for the evening's speakers.
"He's a unique guy and he did a unique thing last night," she told "CBS This Morning."
Eastwood, a fiscal conservative who takes left-leaning stands on social issues such as gay marriage and environmental protections, made waves with conservatives earlier this year when he starred in a Super Bowl spot for Chrysler, a company that benefited from government support. Eastwood, who endorsed Romney earlier this month at a campaign event in Sun Valley, Idaho, and once served as mayor of Carmel, Calif., defended his appearance in the commercial, noting it had nothing to do with his politics.
Inside the convention, the crowd cheered Eastwood's entrance and shouted his famed catchphrase, "Go ahead, make my day." But backstage, stern-faced Romney aides winced at times as Eastwood's remarks stretched on. After his speech, Romney's camp defended Eastwood.