Ms. Rice, 54, a political science professor at Stanford University in California, told an audience of 1,200, “This is a powerful country that has been a powerful force for peace and liberty in this world. I want to see it be that way for well into the future,” in urging a vote for Mitt Romney.
Mr. Ryan later hosted a roundtable at an Italian restaurant in Columbus.
It was Mr. Ryan’s sixth Ohio city visit in six days as he and presidential candidate Mitt Romney kept the heat on in campaigning.
Alluding to the importance of Ohio’s 18 electoral votes in tipping the election one way or the other, Mr. Ryan told his audience that, “you’re the battleground of the battlegrounds.”
Mr. Ryan said Mr. Romney showed leadership qualities in the debate.
“Didn’t Mitt Romney do a great job for us last night," Mr. Ryan said. "Cut through the clutter of all the attack ads and what did we see, we saw a President offering not a single new idea on how to turn things around."
Later in the speech, Mr. Ryan amended himself to say, "The President basically has one new idea: raise taxes even more."
He said Mr. Obama wants to raise taxes on successful small businesses to more than 40 percent when competitor countries overseas are taxing at 25 percent or less and Canada has lowered its corporate tax rate to 15 percent.
The Obama Administration said most small businesses are taxed by way of the income tax that Mr. Ryan was referring to, but that only a small fraction of small business owners pay the top rate.
A spokesman for the Obama campaign in Ohio said Mr. Ryan "doubled down today in Berea by trying to peddle their sketchy tax deal, which includes $5 trillion in tax cuts for the wealthy at the expense of the middle class and a plan to turn Medicare into a voucher program."
"People in Cuyahoga County and across Ohio know that the Romney-Ryan plan includes one set of rules for them and their friends and another set of rules for everyone else," said Jessica Kershaw, press secretary for Obama for America—Ohio.
Ms. Rice was national security adviser during President George W. Bush’s first term and secretary of state in his second term. She was the first black woman to hold the latter job.
She specializes in the Middle East but ignored a controversial moment in the presidential debate when Mr. Romney and Mr. Obama disagreed about whether President Obama blamed terrorism for the Sept. 11 attack on the American consulate in Benghazi, Libya, in which four Americans were killed.
"We’re at a crossroads about what kind of a country we are going to be, and whether you and I who have benefited so much from what our ancestors gave us are going to pass on that same liberty and opportunity to our children and that’s what this election is about," Ms. Rice said.
"We are at a crossroads because we cannot continue to spend money that we cannot afford to pay back and therefore saddle our children with debt. We cannot afford to continue to be a country in which so many men and especially so many women in these hard economic times don’t know if they will ever work again," Ms. Rice said.
She drew on her own life as an example, saying, "Americans have a way of making the impossible seem inevitable." Speaking of her childhood in Birmingham, Ala., in the 1950s, she said she couldn't even go into a restaurant or movie theater, "but her parents have her absolutely convinced she can be president of the United States, and she becomes secretary of state."
Most of the audience were enthusiastically on board the Romney ticket, including many Baldwin Wallace students. At least one student was still undecided, about even whether to vote.
Josh Nees, 22, of Akron, a math major, said he voted for President Obama in 2008 because, “My area’s very strongly into Obama. I jumped on the bandwagon.” This time, he’s not sure he wants to vote.
“I've heard bad things and I've heard good things [about President Obama]," he said. "I just don't know what the truth is.”
Kathy Geraci, 51, a retired registered nurse from North Royalton, Ohio, said the debate performances confirmed she was backing the right candidate.
“Romney was the same as he was in the first debate, which was awesome. Obama actually showed up this time, but he still acted like he didn't want to be there," Ms. Geraci said.
Contact Tom Troy at: email@example.com or 419-724-6058.