mobile phone + password = 2 factor auth?

[Seth Vidal]

I was changing some settings with my mobile phone company and in order to 
change my password they made me use what looks a lot like 2 factor auth:

something I know: my current password
something I have: my phone

I logged in with my current password - then they txt'd me a temporary 
password which I had to type in to verify I was me.

Which got me to wondering - if most people have a mobile phone and/or have 
access to one - why couldn't we use that as the second factor for our 
auth?

I can think of multiple ways to do it:

1. login to a web page
2. click on 'auth me' button
3. it sends you a txt msg
4. you input the password it sent you
5. you get a cert back that you use for auths for a set period of time (24 
hours?)

or

1. login to a webpage
2. download a key
3. it sends you a txt msg which contains a password for that key
4. the key + txt'd password allows you to login for a set period of time 
(24 hours?)


Now, my question is - what is dangerous/silly about this?

-sv