* Cain runs second to Romney in first four states to vote
* Romney sweep would put quick end to nominating fight
WASHINGTON, Oct 26 (Reuters) - Former Massachusetts Governor Mitt Romney leads his campaign rivals in the four states that kick off the 2012 Republican presidential race, according to CNN/Time/ORC polls released on Wednesday.
Barely more than two months before the first nominating contest, Romney has narrow leads in Iowa and South Carolina and double-digit advantages in New Hampshire and Florida.
Conservative businessman Herman Cain, who surged into the lead in some recent national polls but has faced heightened scrutiny in the past week, is in second place in each state.
A Romney sweep of the first four states to cast votes in the nominating race would put an early end to the battle to find a challenger to President Barack Obama in 2012.
But the polls also found there was plenty of room for more changes in the frequently shifting Republican race. Majorities in Iowa and South Carolina said they might change their minds about their votes, and about half in Florida and New Hampshire said the same.
The polls found Romney with a slight edge in Iowa of 3 percentage points, 24 percent to 21 percent, over Cain. His lead was even smaller, 25 percent to 23 percent, in South Carolina. Both leads were within the polls' margin of error of 5 percentage points.
Iowa and South Carolina have big blocs of conservative voters distrustful of Romney, who as governor of liberal Massachusetts supported abortion rights and a healthcare overhaul that was a precursor of Obama's federal law.
Romney has a big 27-point lead over Cain in New Hampshire, which borders Massachusetts and where Romney has a vacation home. He also has a comfortable 12-point lead, 30 percent to 18 percent, over Cain in Florida.
The polls were taken Thursday through Tuesday, following the most recent Republican debate last week.
Libertarian U.S. Representative Ron Paul was in third place in Iowa, South Carolina and New Hampshire. In Florida, former Speaker of the U.S. House of Representatives Newt Gingrich and Texas Governor Rick Perry were tied for third place.
Iowa kicks off the nominating race on Jan. 3, followed by New Hampshire, which is expected to hold its primary on Jan. 10, South Carolina on Jan. 21 and Florida on Jan. 31.
Romney's support was relatively broad across various political and demographic groups. He led easily among self-styled moderate or liberal Republicans, but also led among Tea Party fiscal conservatives in New Hampshire. He tied Cain among that group in Florida and was second behind Cain with Tea Party voters in Iowa and South Carolina. (Editing by Peter Cooney)