* Bachmann falls to fourth place in poll
* Iowa caucuses scheduled for Jan. 3 (Adds details on poll, background)
DES MOINES, Iowa, Oct 29 (Reuters) - Republican White House hopefuls Herman Cain and Mitt Romney are in a tight race in Iowa, which kicks off next year's presidential nominating contests, according to a closely watched opinion poll published on Saturday.
The poll conducted for The Des Moines Register showed Cain, a conservative businessman, with the support of 23 percent of Republicans surveyed. Romney, a former Massachusetts governor, had 22 percent, and Texas U.S. Representative Ron Paul 12 percent in the race to challenge Democratic President Barack Obama in the November 2012 election.
Texas Governor Rick Perry, who has stumbled in debates and on the campaign trail after a fast start, scored only 7 percent support.
The Iowa caucuses will take place on Jan. 3, the first of the state-by-state contests to choose a party presidential nominee.
The poll showed Minnesota U.S. Representative Michele Bachmann fading after running neck and neck with Romney in the June Iowa poll. Bachmann dropped to 8 percent and fourth place in the new poll.
Neither Cain nor Romney has spent much time campaigning in Iowa. Romney, who has just four paid staff and a consultant in the state, has rarely visited Iowa since a second-place finish in the caucuses in 2008 wounded his campaign.
Iowa has a large bloc of conservative voters distrustful of Romney's past support of abortion rights and a Massachusetts healthcare overhaul that was a precursor of Obama's federal law.
Cain's surprising rise has been achieved with a small organization in states that hold early primaries and caucuses.
"One thing I've noticed in my short two months with the campaign is that the more people see of Mr. Cain, the more they like him," said J.D. Gordon, a spokesman for the campaign.
Romney's campaign declined to comment on the poll results.
Former Pennsylvania Senator Rick Santorum, who has spent more time in Iowa than the other candidates and visited more than 70 of Iowa's 99 counties, received just 5 percent support in the poll. Former Utah Governor Jon Huntsman, who has lagged consistently behind his rivals, received 1 percent.
The Iowa Poll was conducted Sunday through Wednesday and was based on telephone interviews with 400 Republican likely to attend the caucuses. The margin of error is plus or minus 4.9 percentage points.
In 2008, the poll correctly predicted wins for former Arkansas Governor Mike Huckabee in the Republican contest and Obama, then a senator, in the Democratic caucus. (Additional reporting by Kay Henderson in Des Moines; Editing by Greg McCune and Peter Cooney)