Found a public radio station out of Cleveland that plays Fallout style blues and swing music and streams it's broadcast at http://www.wkhr.org/information/liveonline.aspx. No advertisemants and few interuptions for local news and weather so a good thing to play in the background while playing.
Sorry but haven't found anything with New Vegas country swing yet for the Marty Robbins fans out there;),
To lazy to go find it, but there's a station I listen to online called 'The sound of The Strip' or something to that effect, it plays alot of amazing Vegasy tunes.
My two favourite streaming stations are http://somafm.com/ and http://www.deezer.com/en/music/radios, each a collection of ad free music streams but neither has the New Vegas feel of yours.