This is a swing state with deep Republican roots. There's a Republican governor and the Republicans have a pretty wide margin in the State House. The US House delegation is also heavily republican. Ohio has 13 Republican House members and only 5 democrats.
There is one from Senator from each party, but remember too that Brown is still in his first term and was elected in the Democratic landslide in 2006. That was an exceptionally bad year for Ohio Republicans, as they were coming off of Taft's disastrous governorship and the Bob Ney scandal, all while there was a national Democratic trend going on. The conservative Democrat who replaced Ney is already gone and Ted Strickland's old seat went Republican in 2010.
I think it's going to be very close here in November. While I would give Obama a slight advantage, it really could go either way. Remember though that even if Romney ekes out a win here, that doesn't get him all the way there. He can't win the presidency without Ohio, but Obama can (as long as he takes Iowa, Nevada and Colorado).