POLL-US Candidate Perry's Gaffe Has Him Down, Maybe Not out

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* 52 percent of Republicans say Perry should stay in race

* Perry, Cain setbacks reshaping race

WASHINGTON (Reuters) - Republican U.S. presidential candidate Rick Perry's disastrous debate performance last week has hurt his campaign, but may not be fatal, a Reuters/Ipsos poll found.

After watching a video of the Texas governor stumbling while trying to name three government agencies he would eliminate if elected, 48 percent of registered Republicans thought less favorably of him, the poll found.

But while 31 percent of Republicans believed Perry should drop out of the race, many more -- 52 percent -- felt he should stay in.

Perry's embarrassing memory lapse further roiled a Republican race already hit by the travails of Herman Cain, who was accused of sexual harassment against four women. Among those polled, 37 percent of Republicans thought Cain, who denies the allegations, should leave the race.

The setbacks to Perry and Cain are reshaping the Republican field of potential challengers to President Barack Obama in the 2012 election. Former Speaker of the House of Representatives Newt Gingrich, once considered an also-ran, has benefited as conservative Republicans cast about for an alternative to the more moderate Mitt Romney.

The Reuters/Ipsos poll had Romney in the lead among Republicans, with 28 percent saying they would vote for him. Perry was fourth with the support of 12 percent, while Cain was second at 20 percent and Gingrich third at 16 percent.

The Texas governor once sat atop national polls and led the money race during the most recent reporting quarter, but a series of stumbles in the debates has eaten into his backing. His fundraising has slowed significantly, sources close to his campaign say.

Perry's campaign went into damage control overdrive Thursday, putting the governor front and center on news shows and allowing him to mock himself in an appearance on comedian David Letterman's late-night talk show.

The online survey was taken among 461 registered Republican voters Thursday and Friday.

Since it was an online poll, typical margins of error do not apply. Despite that, various recognized methods were used to select as representative a sample as possible and weigh the results. If it were a traditional random survey, it would have a margin of error of 4.5 percentage points.

(Reporting by Mark Felsenthal; Editing by Peter Cooney) ([email protected]; +1-202-898-8329; Reuters Messaging: [email protected]))