For Christie, who says he is considering running for president, the speech was the biggest to date before a Southern audience. He would likely need to woo such voters to succeed in 2016.
He cited his ability to work with the Democratic-controlled Legislature in New Jersey to enact pension and property-tax changes as a model for altering the culture of Washington.
"I don't know when it became wrong to go to talk to people on the other side, to respect them, and to become their friends," Christie said, noting his friendship with state Senate President Stephen Sweeney (D., Gloucester). "We can disagree, but if we don't establish relationships, when the real problems need to be solved . . . we won't be able to do it."
Though Christie trumpeted his achievements in New Jersey, he didn't mention that one of them appeared to be unraveling.
This month, he announced a proposal to address a $2.75 billion revenue shortfall through fiscal 2015, partially by slashing the state's pension payments.
He criticized President Obama for sending mixed signals to the rest of the world: drawing a red line in Syria, for example, but not keeping to his word when the country used chemical weapons.
"No one knows where America stands anymore, domestically or around the world," he said.
The Statesmen's Dinner is a high-profile event on the Republican fund-raising circuit: Former President George W. Bush, former Vice President Dick Cheney, and 2012 Republican presidential nominee Mitt Romney are among those who have delivered keynote speeches, said Chris Devaney, chairman of the Tennessee GOP.
Devaney said he decided to invite Christie after watching him speak at an August meeting of the Republican National Committee in Boston.
"It really told me a lot about him as a governor," Devaney said.
He said this year's dinner drew 1,700 guests - the third-most in its 35-year history, behind Bush's 1997 visit, when he was contemplating a run for president, and Cheney's in 2002. (Bush's opponent in 2000, Democrat Al Gore, is a Tennessee native.) The 2014 dinner raised more than $700,000 for the Tennessee GOP, the party said.
"If you're a Republican running in a presidential primary, you have to do well in the South," Devaney said in an interview Friday. "Tennessee is a good place to test your message."
The South represents a key bloc of voters for the Republican Party; South Carolina is the third state to hold primaries in presidential years, noted John G. Geer, a political scientist and pollster at Vanderbilt University.
Christie could make inroads in the South in Tennessee, where Romney carried 59 percent of the vote in 2012 against President Obama.
The state's Republican leaders - Gov. Bill Haslam and U.S. Sens. Bob Corker and Lamar Alexander - are conservative, but "none of them are what you call tea partyers," Geer said.
"If you think about those leaders of the state, Christie isn't all that different," he said.
Christie has traveled to more than a dozen states in recent months, including Arizona, Nevada, Florida, and Maine, mostly in his capacity as chairman of the Republican Governors Association. He helped raise a record $23.5 million in the first quarter of 2014 for the group.
His appearance in Tennessee was a departure from his earlier practice, when he traveled to a number of states but held only private events as he was dogged by national Democrats in the media over the George Washington Bridge lane-closing scandal.
Earlier on Friday, he appeared at a campaign-office opening for Alexander, attended a fund-raiser in Memphis, and mingled with voters with Haslam - who is running for reelection - at a restaurant in downtown Nashville, where Christie posed for a picture with members of a bachelorette party.