* Cain's troubles could open door for rivals in Iowa
* Perry launches new television ads, increases Iowa visits
* Half a dozen candidates battle for conservative support
By John Whitesides
DES MOINES, Iowa, Nov 2 (Reuters) - Republican U.S. presidential hopeful Herman Cain's struggles could open the door in Iowa for rival Rick Perry, who has stepped up his visits and advertising two months before the state kicks off a wide-open nominating race.
Cain's controversy over sexual harassment allegations from the 1990s threatens to erode his support in the state, where he led a key recent opinion poll, and shift the fight for the loyalty of Iowa's big bloc of social conservatives. [ID:nN1E7A10R9]
The former pizza executive has led the half-dozen candidates battling to emerge in 2012 as the top conservative alternative to former Massachusetts Governor Mitt Romney, who has remained steady near the top of the Republican pack all year. The eventual Republican nominee will face President Barack Obama, a Democrat, in the November 2012 election.
Cain already had come under fire in Iowa for saying abortion should be a family decision, and the new controversy chips away at his biggest political asset -- his likability.
"This undermines people's trust in Herman Cain and ultimately it could undermine his chances in Iowa," said Craig Robinson, a former state party official who runs the Iowa Republican website.
Perry, the Texas governor who has floundered in polls but led Republican contenders in third-quarter fundraising, could be in the best position to pick up the pieces from Cain, who has denied ever sexually harassing women.
"Who can break out of the pack?" Robinson asked. "Any of them could. Perry has an advantage because he has resources."
Perry has launched two television ads in Iowa and will spend three days in the state this week. That follows a visit a week ago to appear at a conservative forum and go hunting with influential U.S. Representative Steve King.
He has a lot of ground to make up. The Des Moines Register's Iowa poll showed Perry, who led state and national surveys until a string of bad debates, tied for fifth place with former U.S. House of Representatives Speaker Newt Gingrich at 7 percent.
That put him behind Cain, Romney and U.S. Representatives Ron Paul and Michele Bachmann. But three-quarters of likely participants in Iowa's Jan. 3 caucuses -- the first contest on the road to the Republican presidential nomination -- have no first choice or could be persuaded to switch, the poll found, leaving plenty of room for more shifts in a constantly evolving race.
'DOWN TO THE LAST MINUTE'
"If you want drama down to the last minute, this will be the year for it," said conservative Iowa talk radio host Steve Deace, adding that the Cain controversy could be a blow to his candidacy.
"You live by personality, you die by personality," he said.
Other Iowa Republican leaders have cautioned that the controversy would not necessarily hurt Cain in the state. Iowa Governor Terry Branstad said Iowans are "fair-minded" and would not jump to conclusions.
But he also said front-runners had a habit of fading in Iowa as the caucuses approach. "There have been a lot of ups and downs and that could happen two or three more times," he said.
Perry has battled Bachmann, Cain, Paul, Gingrich and former U.S. Senator Rick Santorum for the allegiance of conservatives, some of whom do not trust Romney because of his past support for abortion rights and for a state healthcare plan with an individual mandate.
After a late entry into the race in August, Perry has spent far less time in Iowa than many of his rivals but has started to spend his cash on advertising and hiring campaign staff.
He has had his own troubles, however, including a video of a recent rambling New Hampshire speech that had some comics suggesting he had been drinking. Perry's most recent television ad, which also went up in New Hampshire this week, tries to turn his poor performances into an asset.
"If you're looking for a slick politician, or a guy with great teleprompter skills, we already have that, and he's destroying our economy," Perry says in a dig at Obama. "I'm a doer, not a talker."
Perry also has been aggressive in taking on Romney, who has led many national polls but has largely skipped appearances in Iowa. On Tuesday in Des Moines, Perry lashed out at Romney and his 59-point economic program as a product of the status quo.
"I'm not much of a status quo person. The establishment's not real fond of me," Perry said. "One of my opponents has a 59-point plan and the first part of that is to preserve the current progressive tax system. To me, the way business is done in Washington is not the solution. They're the problem."
Perry's first television ad focused on his main campaign theme -- his ability to turn around persistently high unemployment as evidenced by his job-creation record in Texas.
A political action committee unaffiliated with the campaign but run by former Perry staff and allies also planned to begin airing a biographical ad in Iowa and South Carolina portraying his rural background and his Texas record. South Carolina also hosts a key early contest in the race for the nomination.
Steve Jackel, a Perry supporter who came to see him in Des Moines, said he still thought he could win in Iowa.
"I think once word gets out, he can win," he said. "The problem is whether or not we can get the word out fast enough."
(Editing by Will Dunham)