It is already the case today that for Chrome and Firefox users, a compromised CA can't easily hijack connections to Google Mail. Not only that, but any attempt to hijack Google Mail connections in the large will run aground on Chrome and Firefox users, who will not only not accept the rogue certificates, but will also alert Google, which will put a gun to the head of the CA.
The feature that enables this is called certificate pinning. It works well for small numbers of high-profile sites, but requires manual intervention on the part of browser vendors.
TACK pushes certificate pinning out to site operators. It works like HSTS: the first connection to a website is trusted, and that connection loads up state that the browser holds. Subsequent connections check for consistency with the first connection. Dynamic pins, or "tacks", make dragnet surveillance of all sites asymptotically as risky as spoofing Google Mail. The attacker is nearly certain to accidentally catch someone with a tack loaded, and at that point the game is up: the attempt to present an otherwise-valid certificate that violates a tack is a smoking gun, to which Google and Mozilla ca respond with their own firepower.
The nice thing about TACK is that it works alongside the CA hierarchy, and even derives some value from it. A tiny fraction of the Internet could adopt TACK and still make life much harder for attackers. The effort required from site operators is small, and the whole system is invisible to end-users.
Fixing the CA hierarchy is a lot less sexy than ground-up rewrites of the whole Internet security model. But the ground-up rewrite is never going to happen, and the incremental fixes are not only doable, but doable by the kinds of generalist developers who are champing at the bit to stick it to the NSA. The biggest security problem on the Internet isn't protocols; it's browser UX.