en. Rob Portman (J. Scott Applewhite/AP) Sen. Rob Portman (J. Scott Applewhite/AP)

The first Republican senator to endorse same-sex marriage has seen his approval rating dip slightly in the month since his announcement.

Forty percent of Ohio voters approve of Sen. Rob Portman's job performance in a new Quinnipiac poll; 31 percent disapprove. Last month, 44 percent approved of his work and 24 disapproved.

The dip is due to a 13-point increase in his disapproval rating among  Republicans. Forty-one percent of GOP voters said they view Portman less favorably because of his shift. Overall, 20 percent of voters think more favorably of the senator now, 25 percent think less favorably and 53 percent say it makes no difference. Portman's disapproval rating with independents is also up slightly.

A narrow plurality of voters in the state favor gay marriage, 48 percent to 44 percent. There is a sizable gender gap, with a majority of women favoring gay marriage and just under half of men opposing it.

"Sen. Rob Portman's reversal on same-sex marriage has cost him a little support in his Republican base, but has little impact among Democrats and independent voters," said Peter Brown, assistant director of the Quinnipiac University Polling Institute, adding that growing acceptance of gay marriage means his position "could help him in the long run."

Portman announced his change of heart in a Columbus Dispatch op-ed, revealing that his son's coming out inspired him to rethink his views. Sen. Mark Kirk (R-Ill.) has since come out in support of gay marriage as well.

"Rob's change of heart was driven by a family issue, and clearly had nothing to do with politics or poll numbers," a Portman adviser said. "He remains focused on the top issues in the minds of Ohioans – our economy, and Washington's out of control spending and debt."

Meanwhile, he's still more popular than President Obama, who garners a 45 percent disapproval to 51 percent approval rating in the poll -- a drop from March, when voters were evenly split on his performance.