Okay, so here are all the things that I think are rational/possible. When Naruto says that he might be able to do it now, I think it can refer to three things:
1) He has enough power to bring Sasuke back.
2) He can complete his Wind Rasengan.
3) He can use the jutsu that Jiraiya was referring to, without having to use the Kyuubi's Chakra (since he can use Senjutsu to compensate)