So what if he's gay or not gay; if people are so worried about who you do, rather than what you do. He's entitled to serve his country in whatever capacity he can serve. It's time to grow up America and wake up to one certainty, that the world is inhabited by all sorts. Is his crime about being gay or that fact people know about it? In my humble opinion, it's a non issue, so now can I have the sports section.
He's almost certainly not gay, though, in the sense that he is not sleeping with men, and has not at least since he entered public life. I think the presidential run should be the end of the "rumors," since there's no way he'd run if he thought it could expose something he's trying to hide, especially since he clearly wants to remain in the senate for years to come.
Given the dual hatred from the left and the hard right, he would have been outed already if there was anything to find. He lives in SC, which unquestionably has the most openly dirty politics in the US. One of his primary opponents this past race said Graham was gay, but obviously couldn't substantiate it (it was just said to inject the idea into voter's minds). People make fun of the way he speaks, but if you're from the Carolinas then his accent and mannerisms wouldn't be unfamiliar to you.
A NYT profile of him a couple years back seemed to suggest that his getting married once his political career got off the ground was hopeless because he literally worked non-stop.