* Obama’s approval rating rises
* Risk of Cain supporters staying home
* U.S. unemployment still high at 9 percent (Recasts with Reuters/Ipsos poll results, adds comments)
By Patricia Zengerle
WASHINGTON, Nov 4 (Reuters) - President Barack Obama’s fortunes rallied on Friday as the U.S. jobless rate eased, his approval rating rose and his Republican rivals battled over harassment claims against presidential hopeful Herman Cain.
Nearly half of Americans now approve of how Obama is doing his job, a Reuters/Ipsos poll showed, and unemployment slipped to 9 percent from 9.1 percent -- good news for the president as he faces a tough 2012 re-election fight with the economy as the key issue.
Rare infighting in the Republican Party, usually known for its unity, also benefits Obama. Cain accused fellow candidate Rick Perry’s camp of being behind news reports the former pizza executive faced sexual harassment allegations in the 1990s.
“Obviously Team Obama wants the Republican field as large as possible for as long as possible,” Republican strategist Ford O‘Connell said. “The more they duke it out, the more ammo Team Obama has going into the general election.”
Democrats have stayed out of the harassment controversy, focusing on Obama’s job-creation plans and keeping campaign attacks on former Massachusetts Governor Mitt Romney, whom Cain replaced at the top of most polls of Republican voters.
“It’s clouding the Republican message right now, so that’s got to be good news for Democrats and they are quite wisely being very quiet about it,” said David Yepsen, director of the Paul Simon Public Policy Institute at Southern Illinois University.
“Napoleon I think said you never interfere with an enemy in the act of destroying himself.”
The Reuters/Ipsos poll showed 49 percent of Americans approve of Obama’s job as president, up from 47 percent in an October poll. His disapproval rating was steady at 50 percent.
While low, the number of Americans who believe the country is headed in the right direction also rose, to 25 percent from 21 percent.
“The more confused and weak the Republican contenders look, the better their opponent Obama looks,” said Ipsos pollster Julia Clark.
The November 2012 presidential election looks to be very close. The Reuters/Ipsos poll showed Obama in a statistical dead heat with Romney if the vote were held today and ahead of Cain and Perry by single-digit margins.
The harassment furor has tarnished the image of Cain, who leads in polls of Republicans nationally and in Iowa, which holds the first 2012 nominating contest on Jan. 3. He has given conflicting accounts of whether women got financial settlements and shouted at reporters seeking answers.
“It’s devastating,” said Democratic strategist Greg Haas, while cautioning that Obama’s team will not want the Republican field to narrow too quickly. “Our side has to watch and see that they don’t create a situation where they end it fast.”
The controversy is an unwelcome distraction from efforts to find one strong Republican contender, just two months before voting starts in the nomination process.
Longer term, it makes the Republicans look bad and could exhaust resources needed to fight Obama.
“The Republicans are trying to avoid a personal, protracted, difficult fight for the nomination. And this seems to be something that’s pouring fuel on a smoldering fire inside the party,” said Christopher Arterton, a professor at George Washington University who has been a Democratic consultant.
Cain’s campaign said his supporters have rallied, giving at least $1 million in donations as the controversy raged. If supporters remain convinced Cain was treated poorly, and they stay home during the general election, it could benefit Obama.
Cain is a favorite of the Republican Party’s conservative Tea Party wing, which has not embraced Romney.
Arterton said Cain’s supporters could decide not to vote or could back him in a third-party campaign if things stay ugly.
“If Cain’s polls go down and his people get very bitter about this, I think you could see the possibility of their deciding that they would mount a campaign in the fall,” he said. (Editing by Alistair Bell and John O‘Callaghan)