What!? Nonono, that would be a bad outcome, to be avoided if at all possible! There are lots of threats against browser-based programs that don't apply to desktop apps. And if there's 2-device authentication, then it's much easier to compromise a matching pair if both clients are in a browser; they're more likely to have vulnerabilities in common. For example, someone could steal an SSL certificate, and MITM traffic on the internet connection that both devices share, replacing both clients with malicious software.

Please, reconsider. The future of Bitcoin depends on there not being any more MyBitcoins or Allinvains. I wrote that online wallet services are an invitation to fraud and theft, a month before the MyBitcoin fiasco. That is still true. Don't encourage people to use them, or there will be more disasters.