ANDERSON, S.C. — On a Monday night in late August, Sen. Lindsey Graham was traveling with a congressional delegation in Africa when the three Republicans who are challenging him in the 2014 GOP primary joined a large and strongly conservative crowd at Rep. Jeff Duncan’s annual Faith and Freedom Barbecue. To listen to Graham’s opponents tell it, that situation — a lawmaker who is far away and out-of-touch — is emblematic of the senator’s relationship with his constituents.