Even if Ryan drops the claim, the damage is done. From PolitiFact, right after Ryan's speech:
Says President Barack Obama broke his promise to keep a Wisconsin GM plant from closing.Paul Ryan on Wednesday, August 29th, 2012 in a speech at the Republican National Convention in Tampa
Did Barack Obama break a promise to keep GM plant open?
Ryan said Obama broke his promise to keep a Wisconsin GM plant from closing. But we don't see evidence he explicitly made such a promise -- and more importantly, the Janesville plant shut down before he took office.
We rate Ryan's statement False.