Mind you, it's probably the best idea.
As always, it's a security/convenience tradeoff - I've gone from needing "something I know and something I have" to "something I know and any one of several things I have".
Your tradeoffs there may vary - if I were a political-dissident/whistleblower/drug-czar I'd probably consider the risk of losing access altogether preferable to opening up additional avenues for vulnerabilities - an NSA-level adversary would probably have a significantly easier time if they knew they only needed to stealthily subvert one of several devices (at least one of which I don't usually have on my person) to get access to all my tfa secured assets, but the additional risk if I'm protecting myself from 4chan-grade griefers or non-network-pervasive internet criminals is - for me - low enough to accept for the additional reliability and convenience of multiple authorised tfa token generating devices.
Backup codes may be a good option if kept somewhere very safe.
I've got at least gmail, aws(/amazon), Github, Dropbox, Zoho, and several TOTP TFA protected WordPress sites on 3 different devices using this method. It definitely works. I see additional devices start to generate the same codes when I add the same seed (so long as their clocks are reasonable synced...)
This is using the Google Authenticatior app on iOS and Android, I _think_ any RFC6238 compliant TOTP app that lets you type in a string to key it should "just work".
I feel reasonably secure about this (as secure as I'm feeling about all the passwords already there in 1password) and I have a huge advantage that changing my phone won't require remembering to disassociate all accounts first if I don't want to lose access to them.
As TOPT works without a back-channel, that QR code stays useable until I manually revoke that key on the respective web site.
Less secure, of course, but my desktop and laptop bypass two factor.
Did you downvote and responded to a thread incorrectly?
(Accidentally deleted a comment of mine, this attempts to copy it)
http://www.itnews.com.au/News/322194,telcos-declare-sms-unsa...
'"SMS is not designed to be a secure communications channel and should not be used by banks for electronic funds transfer authentication," Stanton told iTnews this week.'
https://accounts.google.com/b/0/SmsAuthSettings?LoginInterst...
AND
https://security.google.com/settings/security/contactinfo?pl...