If I was in the NSA (which I am not) I would place a backdoor in the browser themselves, and since the browsers auto-update from the internet anyway, I would change the DNS provider for the machine being watched (remember the DNS settings generally default to that provided by your ISP) to point to the NSA-version of the browser, and then the user would be browsing securely, but after decryption and before display, the payload would be sent elsewhere to be collected.

I don't think this would be particulary hard either. For IE, the NSA can just get MSFT to do it. For Firefox, they can compile from source, and for Chrome, well, they can probably compile from source too, because they probably have access to the build source of Chrome, with or without GOOG mgmt knowledge.

Can anyone come up with a (technical) reason the NSA could not be doing this?