Just grabbed a phone with 4.1. Most questions talk about the Google Listen app, but I can't find it. Did google remove the "podcasting" feature from their Play suite?
Yes, on August 3rd 2012 Google Listen was discontinued and is no longer available on Google Play. If you already have it, it will continue to work, but on November 1st 2012, the Podcast Search will cease to work.
This project was very limited in functionality anyway. There are other apps out there that are updated and actively worked on. I think the last time Google Listen was updated was a couple months after it came out in 2009.
A lot of the podcast apps out there now can make use of the "Listen Subscriptions" folder that is in Google Reader. This is where Google Listen stored your subscribed podcasts. I continue to use Reader to store my podcasts in this location, then I import it to the player on my phone.