There were reports that Barnes was invited to play this summer. According to this article, the following have received invites:
http://www.sbnation.com/nba/2013/5/2...wall-mini-camp
Kyrie Irving, John Wall, Damian Lillard, Ty Lawson, Kemba Walker, Klay Thompson, Harrison Barnes, Larry Sanders, Gordon Hayward, Derrick Favors and Brad Beal. I am sure more invites have been leaked since then, and more will come once the finals are over.
I think Barnes' chances of making a team are probably best in 2014 as USA Basketball, in the last cycle, used the World Championships as a proving ground for the Olympics, which this country seems to hold in higher esteem - while the rest of the world seems to consider the Worlds, now the World Cup of Basketball, to be the more prestigious tournament. The Worlds are definitely a better pool of teams. The 2014 World Championships team will likely be 100% newbies, with maybe some more experienced Team USA leaders - Stephen Curry, maybe, Anthony Davis?
The 2016 Olympic team will have many fewer available spots depending on who is healthy and interested. You'd assume that guys who won't play in 2014 but will be interested in 2016 include Lebron, Durant, Westbrook, Harden, Love, and maybe Deron Williams. That leaves 6-7 slots and you have to figure they may get filled by other guys like Curry or those not listed above, like Paul George, etc .
I think Barnes, unless he really approaches All Star level next season, is a long shot to make either team. I don't think his past interactions with Coach K will matter at all. If they did, he wouldn't have gotten a camp invite. K has way bigger fish to fry then to worry about getting dissed by the Pigeon, dirt off his shoulder.