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“Ohio voters have tended to like those kind of candidates, so I think Brown has in some ways offset his more liberal tendencies that might put him a bit out of the mainstream, at least for Ohio swing voters,” he said.

Many also view Mr. Mandel as a weak candidate who, at 34, lacks the experience and name recognition of Mr. Brown.

In Wisconsin, polls are mixed between Ms. Baldwin and the GOP front-runner, former Gov. Tommy G. Thompson, to fill the seat of retiring Sen. Herb Kohl, a Democrat. Ms. Baldwin holds significant leads over all other GOP candidates, and Democrats say their voters’ enthusiasm in Wisconsin is high this year, fueled by the June recall election of Gov. Scott Walker, a Republican.

Republicans point to Senate races in Montana, Nebraska and North Dakota — seats held by Democrats — where Republican candidates lead in the polls. Senate races in New Mexico, Missouri and Virginia, also Democratic seats, are too close to call.

“From red states to purple states to even blue states, Senate Republicans are on offense and well-positioned in a range of key Senate races across the country,” said Brian Walsh, a spokesman for the National Republican Senatorial Committee, the fundraising arm of Senate Republicans.