the u.s. supreme court will hear oral arguments tuesday in a case .
the question at the core of obergefell v. hodges is one of the most consequential debates of the early 21st century , and one that is already helping to shape the 2016 presidential race , led by roberts .
appointed to the bench by president george w. bush , roberts has a solid conservative record and would seem an unlikely vote to support a constitutional right to same-sex marriage .