Former secretary of state Condoleezza Rice (Luca Ghidoni/Getty Images)

In a question-and-answer session following her speech at Harding University here, Rice said she would not be Mitt Romney’s running mate.

“Thank you for that enthusiastic response, but no,” she said.

In a CNN/ORC International poll released this week, Rice led the veep field with 26 percent of Republicans and GOP-leaning independents wanting the former secretary of state as vice president. Rick Santorum placed second, followed by Florida Sen. Marco Rubio and New Jersey Gov. Chris Christie.

“We’ll find a good running mate,” she told the crowd of nearly 4,000.

They definitely wanted her to say yes. In fact, they want her to run for president.

“She’d bring back integrity and what the office of president means,” said Fred, an elderly man who said he wouldn’t provide his last name to a representative of the “liberal media.” But he did have a favor to ask: “If you get to ask her a question, ask if she still plays piano in her church.’’

The crowd at the Christian university about 50 miles north of Little Rock seized on Rice’s every word.

Rice, now the Thomas and Barbara Stephenson senior fellow on public policy at the Hoover Institution at Stanford University, peppered her speech with policy wonkiness and American optimism. It was part memoir, part foreign relations lecture. Rice’s concerns ranged from K-12 education crisis to the war in Afghanistan, with the Arab Spring sandwiched in between.

“I hope we have the staying power to finish what we have begun,” she said of operations in Afghanistan.

But she called the need for a better education system possibly the “greatest national security threat.”

With some students unable to read by fourth grade, the United States is creating a situation that may not be reversible. Rice said that teachers should demand more excellence from their students. She also thinks teachers should strive to become better, and if they don't, they should find new jobs.

(Does Rice maybe want a shot at education secretary?)

She is also concerned that the United States isn’t taking action in Syria because it lacks a strategy for the country.

What Rice didn’t deliver Thursday night was talking points and partisan rhetoric.

The lengthy question-and-answer segment showed the relaxed side of Rice. She laughed when asked about the late Libyan ruler Moammar Gaddafi’s crush on her and the song “Black Rose in the White House” that he had composed for her.

Vladimir Putin, with his steely cold eyes, was the most intimidating world leader she met, she said, but she stressed that she did not let him get the best of her. When he stood and peered over her at a meeting, she stood, too, towering over him by a few inches in her high heels. Apparently, a new respect was forged.

She even offered simple advice to students in the audience about succeeding: Write clearly, speak well and attempt something hard. Easy gets you nowhere. Oh, and don't be afraid to change majors.

Of course, Rice discussed the 2012 election.

“Americans are anxious about the role of government, the size of government and the intrusion of government,” Rice said. “Government is trying to do too much. Ultimately that may be the real sleeper issue in the campaign,” she added, showing that she hasn’t lately been anywhere near a campaign trail, where that discussion is front and center.

Rice hit a nerve when she said she wants a candidate to tell the truth about what the country can and can’t afford and what entitlements must go. The crowd applauded wildly.

And hey, Romney and Obama, Rice doesn't want to hear these words: “On day one, I will....”

“No, he won’t,” she said tartly. “Barack Obama said he would close Guantanamo. It’s still open.”

Suzi Parker is an Arkansas-based political and cultural journalist and author of “Sex in the South: Unbuckling the Bible Belt.” Follow her on Twitter at @SuziParker.