Mitt Romney would love a debate like the last one. President Barack Obama most certainly would not.

Twenty-one days before Election Day, Debate Two comes as both candidates seek to break out of a neck-and-neck national race with the type of debate performance and vision that could help sway a narrow band of undecided voters in a handful of crucial states.

Mr. Romney needs to reinforce his case that he’s an agent of change and raise further doubts about Mr. Obama’s economic tenure in the face of some positive signs of recovery. Mr. Obama must reverse the corrosive story line ignited by his lame performance in the first debate and make a convincing case for four more years of his presidency.

The president has promised not to be the disengaged Mr. Obama of Debate One. Yet he won’t be the grinning, eyes-to-the-sky Joe Biden of last Thursday’s vice presidential face off, either. Mr. Obama’s approach is more likely to resemble the methodical, persistent and affable debating style of Paul Ryan, Mr. Romney’s running mate.

Still, Mr. Obama says he was too polite in the first debate. His aides promise a more aggressive president this time.

And Mr. Romney needs to sustain the apparent connection he made with many voters in his last encounter with the president, without becoming defensive in the face of Obama’s more assertive stance.

It won’t be easy for either.

The debate will be conducted as a town hall with the candidates fielding questions from audience members selected by the Gallup polling group for their undecided views. An aggressive approach usually doesn’t work in such a format, where candidates need to connect with the questioners first before turning on their opponents. Four years ago, Mr. Obama’s rival John McCain entered that election’s town hall debate looking to upend a race going in Obama’s direction. Mr. McCain needed to raise doubts about Mr. Obama, but his hard-hitting tone seemed off key in the midst of earnest audience questions.

Mr. Romney has been testing the town hall format in recent campaign appearances, opening his rallies to questions from the audience. Mr. Obama has done little of that in this campaign, a stark contrast from the 2008 primaries when the give-and-take with audiences was an essential part of his introduction to voters.

Mr. Romney aides concede that taking questions from friendly supporters is not akin to a town hall debate. Moreover, they acknowledge that the format helps Mr. Obama, who is perceived as more personable by the public, and they are aware of how he got the best of Mr. McCain four years ago.

The challenges for Mr. Obama:

This debate comes with Mr. Obama’s approval ratings hovering around 50 percent. The economic and fiscal picture is mixed. Since the last debate, the government announced that the unemployment rate had dropped to 7.8 percent after 43 months of being above 8 percent. Still, the Treasury Department on Friday reported that the federal deficit for the 2012 budget year that just ended was $1.1 trillion.

Mr. Romney, as he did in the first debate, will focus on the downside of the ledger 23 million people struggling for work or better jobs, 15 percent of the people living in poverty, a rising national debt. Obama will have to draw attention to the improvements under his administration, echoing the points made in a television ad released Monday that emphasises hiring by the private sector, including more than 5 million jobs created in the last 30 months.

On another front, Mr. Obama and his administration have struggled to explain the circumstances that led to an attack on the U.S. Consulate in Benghazi, Libya, that killed four Americans, including U.S. Ambassador Chris Stevens. A congressional hearing last week revealed past decisions by the State Department not to increase diplomatic security in Libya.

In his debate last week, Mr. Biden declared that “we weren’t told” about the requests for additional security, prompting Mr. Romney to accuse the vice president of “doubling down on denial” and forcing the White House to explain that Mr. Biden was referring just to the White House, not the entire Mr. Obama administration.

The challenges for Mr. Romney:

Illustrating Mr. Romney’s expectations burden, a Pew Research Centre poll found that 51 percent of voters expected Mr. Obama to win the first debate compared to 29 percent who thought Mr. Romney would win. This time, a new Pew poll shows expectations for both candidates are nearly evenly divided, with 41 percent expecting Mr. Obama to prevail compared to 37 percent saying Romney will likely win.

Mr. Romney can expect to be challenged more forcefully on his economic plan than he was two weeks ago. Both Mr. Romney and Mr. Ryan have declined to specify how they would be able to cut federal income tax rates by 20 percent across the board without raising the deficit. Mr. Obama will argue that cutting taxes for wealthier taxpayers can only result in higher taxes on the middle class, a notion that Mr. Romney disputes.

Mr. Romney must also be ready to defend the more moderate political image he demonstrated in the first debate. Mr. Obama is eager to portray Romney as an out-of-the-mainstream conservative and will force Mr. Romney to explain himself on health care and changes in the government’s regulatory regime, positions that Mr. Romney recently softened after taking hard lines during the Republican primaries.

In the end, while the debates are attracting millions of viewers, the target audience for each campaign is becoming an increasingly small number of fence-sitting voters in a handful of battleground states.

It’s a loud megaphone for a small crowd.

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