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“When George was in the United States Senate, he voted to privatize Social Security, and that would have been a huge catastrophe,” Mr. Kaine said. “I will fight efforts to privatize Social Security to my last breath.”

The looming $500 billion in defense cuts that resulted after Congress reached a deal to raise the debt ceiling last summer has fast emerged as a central campaign theme for Mr. Allen, who consistently points to Mr. Kaine’s support for the deal.

But the so-called sequestration cuts were never intended to take effect: As part of the deal, about $1 trillion of additional cuts over the next decade, to be divided equally between defense and domestic spending, would kick in next year if a congressional supercommittee failed to reach a deal, as an impetus for the group to act. But there was no deal, and, absent further congressional action, they will start to take effect next year. Both Mr. Allen and Mr. Kaine say they want to reverse the cuts.

“The way you pay for it, Tim, is with a vibrant economy, where people are working and businesses are prospering — not higher taxes,” said Mr. Allen, who cited the repeal of Obamacare, elimination of inefficiencies and redundancies in the government, and using the country’s energy resources to generate hundreds of thousands of jobs created and more than $1 trillion in government revenue.

“The question was about sequester, and I did not hear any specifics from George other than we should repeal the Affordable Care Act, which the [Congressional Budget Office said] will increase the deficit, not reduce the deficit, and it would put us right back into the mix of a partisan battle we’ve been having for the last three years,” Mr. Kaine said.

Mr. Kaine reiterated his plan of allowing the Bush-era tax cuts to expire for incomes of more than $500,000, taking away subsidies for the country’s largest oil companies, and allowing the federal government to negotiate with pharmaceutical companies over prescription-drug prices for a seniors’ entitlement program.

Both candidates touted bipartisan accomplishments during the debate — but in their closing statements, accused the other of being too partisan to serve in Washington.

“If Tim’s in, he’ll be right in there for the same folks he’s been campaigning for all these years when he was chairman of the Democratic National Committee, ignoring the needs, the dire needs, of people in Virginia,” Mr. Allen said, saying that he wanted to see change in Washington and “positive, constructive ideas.” “Anybody who pays taxes should be on our side, unless you want to pay higher taxes.”

Mr. Kaine described Congress as an “ankle weight” on the economy — and that electing Mr. Allen would only make it worse.

“When he was governor, he famously said, his job was to enjoy knocking Democrats’ soft teeth down their whiny throats,” he said. “We need folks who know how to compromise and work together.”