Not sure if you have already figured this out.
I got it to work on my site by doing the following.
Extensions > Module Manager
click the square button next to Polls and click on copy icon at top right of page.
look for Copy of Polls under Module Name
click to edit the module
Change the name to say iphone Poll (you will need to make 3 more copies just like this, one for each template)
or you can leave it as Polls (if you want to show the title) You can have the same name on each of the 4.
Enabled (yes)
position mj_iphone_middle
I am showing the main menu on the iphone, so I had
Menu Assignment (*)Select items from List
and highlighted Home under Main Menu
saved
viewed the site with FireFox and User Agent Switcher and there was the Poll
It allowed me to choose and then told me I had already voted today
which was true.
Does that help?