XThe new Sen. Graham had barely served a week in office since her brother’s death before making her intentions known. “Sounds like the field is taking shape, and we’ll let the voters in South Carolina decide it,” Thune said. Russell announced he's running for the Senate in South Carolina in the special primary election. In her interview with Hannity, Graham acknowledged that while the filing window to run begins on Tuesday, it runs through July 28. The memorial services for her brother in Washington, D.C. and in South Carolina are July 28 and July 29.