His push has only been going for a couple of weeks, but surprisingly, they haven't managed to screw it up yet (it's still early, though.)
I agree that a Punk/Axel feud seems obvious at this point. As stated, Punk doesn't show at Payback and Axel takes his place and gets his first pin fall victory by defeating an accomplished star like Jericho. He perhaps does it again at Money In The Bank.
During all of this, we hear nothing of Punk and all the while, Axel starts knocking Punk and saying that because he couldn't bother to take a twenty-thirty minute drive to the arena and face Chris Jericho like a man, he stepped up and took care of it for him. He says to Heyman that he doesn't need Punk anymore because he has him. Heyman doesn't exactly join in and agree, but he remains silent and has a look on his face where he's giving it thought and not exactly disagreeing. Punk returns eventually and confronts Axel (and Heyman) over the comments made about him. He says that when he walked away from WWE, he needed to walk away from all of it and he hasn't even bothered to watch or otherwise keep up with any of the shows or happenings since then. He was also away on vacation and not even in Chicago when the Payback PPV came to town. He tells Heyman he should check with him next time before accepting challenges for him that he isn't even aware of.
Axel gets in his face and Punk doesn't back down, but Heyman calms down the two of them. He perhaps gets them to work together for a short time but this leads to a situation where Heyman chooses Axel over Punk and thus Punk's full official baby face turn is complete. Hopefully, this transitions into a HHH feud for Axel (when HHH returns) and a Brock feud for Punk. That's another story, though.