The whole 200X and 20XX thing has probably been a thorn in Capcom's side for a while now. As the characters say, in the first two Megaman games, the date was given as 200X, indicating it was somewhere between 2000 and 2009, which I'm sure seemed plenty far in the future in 1987. But, as much science fiction soon discovers, the future comes faster than you'd think, so they made the decision to change the system to 20XX in Megaman 3.
So while this doesn't preclude the possibility that the game takes place in the first decade of the new millenium, to me it would suggest that it's actually 2010, and with one year taking place between each game, based on their production dates, that would suggest that Megaman 6
takes took place in 2014.
Of course, all of this is a moot point, since when Capcom remade the first Megaman game in Megaman Powered Up for the PSP, they changed the date to 20XX, pushing the appearance of humanoid robots further in the future.
I love Mega Man's line of drool.