iOS hacker and jailbreak wiz Winocm, who is currently working to jailbreak iOS 6.1.3 as well as 6.1.4 has given a "definite ETA" on making his efforts a tangible success "before 2014." Thus, it would seem that he is indeed making strides, and although many iPhone, iPad and iPod touch users are currently waiting and hoping for news on a possible iOS 7 jailbreak, this is certainly a good day for the jailbreak scene in general.
Back when the Evad3rs team came through with the untethered jailbreak for iOS devices up to and including iOS 6.1.x, it was later stated by those behind it that a jailbreak for iOS 6.1.3 would not be pursued because exploits would instead be saved for the more pressing issue of iOS 7. This hasn't stopped other well-known developers from trying to find a solution, and developer Winocm has just thrown out a tweet suggesting he is getting there.