Carroll said he does not "make major decisions hastily."

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"If I believe I could provide a serious alternative to Senator Graham for the voters of South Carolina, and I can find the financial and moral support to join me in that effort, then I will take those next formal steps needed to do so," he said. "Someone needs to be the Conscience of South Carolina's Voters during the 2014 Primary. I hope I can accept that challenge."

Graham, who has broken with the conservative base of his party on some tax issues as well as immigration and climate change, may be vulnerable to a potential primary challenge. But it's unclear how well an openly gay candidate could do running as a conservative challenger in a South Carolina Republican primary.

