The Ohio Senate race between former Republican Congressman Rob Portman and Lieutenant Governor Lee Fisher remains very close.

The latest Rasmussen Reports telephone survey of the state’s Likely Voters shows Portman picking up 43% of the vote while Fisher earns 39%. Four percent (4%) would vote for some other candidate and 13% more are undecided.

Portman’s support has stayed within a very narrow 42% to 44% range since February. During the same period, Fisher’s support has stayed within a 39% to 43% range. The two men were in a virtual tie earlier this month and early May.

While Portman holds a double-digit lead among men in Ohio, Fisher holds an edge among women. Among voters in the state not affiliated with either major political party, Portman holds a double-digit edge but a large number of unaffiliated voters are committed to either candidate.

In Ohio, 57% favor repeal of the health care reform law, which is slightly higher than results found on the national level. Thirty-eight percent (38%) oppose repeal of the law. Those numbers include 43% who Strongly Favor repeal and 27% who Strongly Oppose it.

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The statewide survey of 500 Ohio Likely Voters was conducted on June 29, 2010 by Rasmussen Reports. The margin of sampling error is +/- 3 percentage points with a 95% level of confidence. Field work for all Rasmussen Reports surveys is conducted by Pulse Opinion Research, LLC. See methodology.

Portman picks up 77% support among those in the much larger group who Strongly Favor repeal of the law, while 68% of those Strongly Opposed to repeal back Fisher.

Portman is viewed Very Favorably by 19% of Ohio voters and Very Unfavorably by nine percent (9%).

Fisher earns Very Favorable reviews from 19% and Very Unfavorable opinions from 14%.

At this point in a campaign, Rasmussen Reports considers the number of people with a strong opinion more significant than the total favorable/unfavorable numbers.

Despite the ongoing oil leak in the Gulf of Mexico, 62% in Ohio still support offshore drilling, which is consistent with results found on the national level. Fifty-one percent (51%) in Ohio also favor deepwater drilling.

On another topic, 37% of Ohio voters give President Obama good or excellent ratings on his handling of the situation in Afghanistan, but nearly the same number (35%) give him a poor rating.

Forty percent (40%) of Ohio voters say it is not possible for the U.S. to win the War in Afghanistan, while 34% disagree. Another 26% are undecided.

Forty-eight percent (48%) of Ohio voters now approve of how Obama is handling the role of president, while 52% disapprove, showing little change from earlier this month. These results are comparable to Obama’s ratings nationally in the Rasmussen Reports daily Presidential Tracking Poll.