Frodo does indeed challenge Sauron for control of the Ring, at Mount Doom:
'I have come,' he said. 'But I do not choose now to do what I came to do. I will not do this
deed. The Ring is mine!'
The "not yet" is, I believe, a harbinger of this. The Ring's influence on Frodo is obvious and growing as they first get closer to Mordor and then after they enter and proceed to the Crack of Doom. We see this in his seizing of the Ring back off Sam after Sam rescues him, and in the effort it takes to drag himself across Mordor.
Galadriel told Frodo what would happen should he attempt to take the Ring for his own and use it to its full powers:
'I would ask one thing before we go,' said Frodo, 'a thing which I often meant to ask Gandalf
in Rivendell. I am permitted to wear the One Ring: why cannot I see all the others and know the thoughts of those that wear them? '
'You have not tried,' she said. 'Only thrice have you set the Ring upon your finger since you knew what you possessed. Do not try! It would destroy you. Did not Gandalf tell you that the rings give power according to the measure of each possessor? Before you could use that power you would need to become far stronger, and to train your will to the domination of others.
i.e. he would be destroyed (presumably mentally rather than physically) and that he needed to become far stronger. Neither of these were true before Frodo's claim in Mount Doom, so we can only assume that it was due to the Ring's influence - it wasn't his rational mind, but rather the Ring trying desperately not to be thrown to its destruction.