Probable reference to the Cole Porter song "Don't Fence Me In" that describes a cowboy's need for space to roam and a lack of borders.
Although originally written for an unproduced 1934 musical, "Adios Argentina," Roy Rogers eventually performed it in the 1944 film "Hollywood Canteen."
Could also be a reference to Thin Lizzy's "Cowboy Song", especially given that Craig has mentioned in interviews the influence that Thin Lizzy has had on The Hold Steady.
The previous part of the line ("The carpet at the Thunderbird has a burn for every cowboy that got fenced in") references the Thunderbird Motel - an Indian-themed hotel in Minnesota.
from Stevie Nix