I am never sure just how much point there is to opposing such bills, due to my assumption that intelligence agencies always have and always will have all the indiscriminate access to domestic communications that they want. I think even publicised history provides more than abundant examples of that.
If there is a real fight, it is over criminal procedure, rules of evidence, and other things useful in more banal dealings with law enforcement, and thus having some bearing on the juridical outcome in the event that one is prosecuted (or persecuted) on the basis of some illegal surveillance technique. In other words, you could get acquitted of dealing drugs if the state's main evidence against you is something obtained through warrantless electronic surveillance, and that surveillance is illegal. And that's important.
But why is it important? It's important because it's small stuff, not the kind of stuff governments would throw national-level resources like NSA supercomputers at. So, the argument is really about the gaps, not the fringes. As far as terrorism and national security-type activities go, it seems to me they already have unlimited _de facto_ authority, capability, and inclination to spy on you all they want, and that this has more or less always been true.
Thus, I find that the rhetoric is a bit off. This isn't about stopping the government having "access to your e-mails". They already have that, in principle. With enough initiative and spiritual commitment, they can track you, read your e-mail, and listen to your voice communications. The real objective ought to be framed more precisely, perhaps something like: "There shouldn't be a law that goes out of its way to grant unto pedestrian police the formal sanction to employ surveillance capabilities hitherto the province of spooky intelligence agencies".
However, that's a lot harder to sell.