It's kind of incredible to see a U.S. President talking about an issue as technical as ISDS. Check it out at 10:48 and 19:10 of this video. Putting aside the argument about whether ISDS is good or bad, I think he is making a mistake in the way he is presenting the issue. (Although I suppose you could argue that presenting it the way I think he should, set out below, would be the real mistake!) At around 20:12 or so, he says there is "zero chance" the U.S. would be sued on the basis of our financial regulations, food safety regulations, or environmental regulations. That's pretty clearly not true, and I'd be surprised to hear any ISDS supporters defend that claim. The only real questions are when and how often we will be sued on this basis. (TransCanada has thought about suing under NAFTA Chapter 11 based on the failure to approve the Keystone pipeline, and may decide to bring the claim at some point.) Sometimes the U.S. discriminates against foreign companies on the basis of nationality, so we could certainly be sued for that. But the bigger issue is the "fair and equitable treatment" obligation, under which we could be sued even if we are not discriminating in that way.
Of course, a lawsuit does not necessarily mean a successful claim, but the suggestion that the U.S. will never lose an ISDS case is not very credible.
In contrast to President Obama's take on ISDS, I think Ted Posner (an ISDS supporter) hits the nail on the head when he puts the issue this way (from Inside U.S. Trade):
"Why should any government get a free pass because it deems a particular level of protection appropriate, not based on science, and not based on evidence, but just based on a subjective sense of what it feels is appropriate?" Posner said. "Why shouldn't that subjective judgment be subject to the obligation to accord fair and equitable treatment and other investment-related obligations?"
That's the issue that all governments, including the U.S., really need to think about. In those instances, and there are plenty, where your actions are not based on science or evidence, or are otherwise arbitrary, should an international tribunal review those actions and award damages to the affected foreign investors? It's easy to be for such rules in theory, as most people believe they regulate properly as a general matter. But as ISDS litigation continues, and the lawsuits and awards proliferate, governments may think differently about this. We're already seeing a change in viewpoint, and each new case is likely to push that further.
And just to be clear, there's a difference between this kind of review, on the one hand, and a review that considers whether your actions were protectionist, on the other hand. The latter does not interfere much with your regulatory autonomy; the former is pretty intrusive.