Haraz N. Ghanbari, File, Associated Press
FILE - In this May 5, 2012 file photo, President Barack Obama arrives to speak at a campaign rally at The Ohio State University,in Columbus, Ohio. In this critical presidential battleground, Republicans hope 2010 is the best predictor of this year’s elections. Democrats hope it’s 2011. No state saw a more sweeping GOP victory in the 2010 midterm elections than Ohio, but that led to a setback when voters rejected an anti-union law a year later. All this forms the backdrop of the race between President Barack Obama and GOP challenger Mitt Romney in a state with a history of voting for the presidential winner.

CINCINNATI — President Barack Obama's Cincinnati visit Monday highlights the battleground within the battleground.

Obama in 2008 became the first Democratic presidential candidate to carry Hamilton County since 1964, getting nearly 30,000 more votes than Republican John McCain. That helped him win Ohio, which has been crucial to Republican presidential hopes.

But in the 2010 elections, Republicans Rob Portman, for U.S. Senate, and John Kasich, for governor, both carried Hamilton County while winning statewide.

"Southwest Ohio is important for Democrats," said Chris Redfern, chairman of the Ohio Democratic Party.

Cincinnati has a strong Democratic base led by a Democratic mayor, and Redfern said the party hopes to do better in Hamilton County's suburbs and neighboring areas. But the crescent of suburbs in the fast-growing counties north and east of Cincinnati has become a bastion of votes for Republican candidates, helping counter heavy Democratic advantages in Cleveland and northeast Ohio.

"We've got a lot of great Hamilton County Republicans living in Butler, Warren and Clermont counties," said Alex Triantafilou, the Hamilton County GOP chairman.

He likes Mitt Romney's chances of returning the area to the Republican side this year. He said the Romney campaign organized early, and he expects Romney to get help from tea party groups that have been particularly active in the Cincinnati region.

A wild card could be Romney's choice of running mate. Portman, from the Cincinnati area, is widely believed to be on the short list of contenders. He was headed Monday to Lebanon, in Warren County, to promote Romney and critique Obama's visit, which was to include a "town hall" session at Cincinnati's Music Hall.

Obama's 2008 campaign made a statewide effort to pick up votes in even Republican-dominated areas, and has signaled that's the same game plan this year. The campaign has field offices up and running in Middletown in Butler County and Mason in Warren County, plus ones in Cincinnati, Dayton and some Dayton suburbs.

Obama and Mitt Romney have made multiple visits to Ohio in recent weeks, with Romney touring a Cincinnati manufacturing plant and holding a fundraiser last month.

"I expect this part of the state to get a lot of attention," Triantafilou said.

Florida's former Republican Gov. Jeb Bush is scheduled to be in Butler and Warren counties on Wednesday, while Romney is in northwest Ohio. Vice President Joe Biden last month canceled a planned trip to Butler County, but is to return to Ohio on Thursday at a yet-unannounced place.

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