She said she supports eliminating it to pass Donald Trump’s SAVE America Act. Darline Graham was appointed by South Carolina Gov. Lindsey Graham backed keeping the Senate filibuster even as Donald Trump urged the GOP to eliminate it. I’m willing to stay through recess to get it done,” Darline Graham said during Monday’s debate. Darline Graham also said she could focus more on domestic issues than her late brother did if she wins a full six-year Senate term.