Tobi decided to go ahead with the Moon's eye plan after Nagato died. Since he no longer had his ace in the hole (meaning the one who could rev Madara), he decided to hurry things along without him. It wasn't that he betrayed him, but rather altered his plans to account for the real madara not being there.
The war was not part of his plan until reviving the real Madara was out of the question. Real Madara confirmed that the war was not part of the plan, but he knew Tobi was doing it for a reason. And Tobi was not mad about seeing Madara because he was scared to face him after betraying him, but rather he was pissed off that Kabuto revived him since it was his plan all along to revive him.
Bottom line? I don't think Tobi betrayed Madara. I think he was doing his best to complete the plan with all the misfortunes that fell upon him. Not only did he loose Nagato, the one that was supposed to revive Madara, but he also was shown an Edo'd Madara that would have halted his plan even if he still had Nagato in his ranks.
Having the Juubi's chakra in him might increase, or eliminate, the time limit imo.
