I think someone linked upthread about large fines that the Australian ASA equivalent had introduced, but their rules seem equally as fuzzy as ours so I don't think they will be easy to enforce. I think fines are a strong possibility though, as much for the deterrent factor as anything else, and I think they would be focused on the brands, who would then have to clearer with their bloggers about what they expect in terms of disclosure.
There is still a place for some self regulation with influencers calling out others that don't play by the book, and as disclosure becomes more widespread it perversely may become more attractive to fledging influencers as it may make them appear more successful (and therefore more attractive as a collaborator) to brands than if they didn't have any sponsored content.
And then of course like any industry you will get some 'rogue traders' who just refuse to play by the rules. But those ones rarely become hugely profitable in the long run, or eventually fizzle and go out of business because people don't trust them.