Congresswoman Nancy Mace (R-S.C.) isn’t hiding her interest in possibly running for South Carolina Sen. Lindsey Graham’s (R) seat following his sudden death on Saturday night.Asked if she’d “eventually” consider campaigning for the Senate veteran’s spot during a Sunday morning appearance on “Fox News Live,” the lawmaker said right now she’s focused on serving the people of South Carolina but was open to the idea.“We’re all still sitting here shocked and stunned that this has happened,” she said, before adding, “I’m never gonna shut the door. I love the people of South Carolina. You only live once and, you know, if the people of South Carolina would like me to serve in that capacity, I’ll certainly take a look at it.”Up for reelection in the reliably red Palmetto State this November, Graham was more or less guaranteed to win his fifth Senate term this midterm cycle.It’s unlikely Mace would have a smooth path to snagging Republicans’ slot in the general election, however, having finished fifth place in South Carolina’s GOP primary for governor last month. Talking about how she’ll be honoring Graham’s legacy, the outgoing legislator told Fox News she “always envisioned” the senator “would live to 100,” serving South Carolina “for decades” like the late Sen. Strom Thurmond, who made it to one century old before ending his 48-year Senate career in 2003. The pro-segregation senator died just six months after leaving his post.Graham’s office announced he had died of a “brief and sudden illness” Saturday night after emergency services were called to his Washington, D.C., residence around 8:30 p.m. to respond to a person suffering chest pain.With Graham’s seat vacant, Gov. Henry McMaster (R) will appoint someone to serve out his term. Meanwhile, Republicans will hold a special primary election on Aug. 11 to choose who will face Democrat Annie Andrews in the general.During a Sunday appearance on “Meet the Press,” President Donald Trump said he already has a “great” person in mind to inherit Graham’s legacy but that it was still “too soon” to reveal exactly who.