Hasn't NaCl been abandoned? On top of the annoying browser incompatibility, this is also a pretty embarrassing case of Google's left hand not knowing what the right hand is doing.
I remember when inbox launched it could be only used under chrome/chromium. Then somebody changed their user agent in firefox to chrome and magically it started working just fine. So you might want to try that.
Looks like the first hurdle is that it's relying on the deprecated document.registerElement API from an early draft of the Web Components specs, which prevents the app from booting in Firefox.
Either the polyfills aren't being shipped or their feature detection is broken, because I get "document.registerElement is not a function" in Firefox Nightly with a spoofed UA string, and I get marginally further if I turn on our experimental native support for Web Components: http://imgur.com/a/TgnrQ
Polymer's polyfills don't work very well, for what it's worth. Sometimes they get confused if things don't load from the network in the order they expect and start eating up gigabytes of RAM and all your CPU...
I believe Inbox had major performance issues in non-Chrome browsers at launch, which was something they fixed in the weeks following its initial release. Once those were fixed, it was opened up to other browsers.
The Firefox bug was trivial to fix, but nobody at Google bothered to report it. If they had, it would have been a non-issue by the time that Inbox was released.