The FCC has a pretty wide mandate, so yeah the lawsuits would be the biggest stumbling block.
If their board of commissioners wanted to, they could reclassify all ISPs tomorrow and assert their authority. If however, their reclassification was overturned, it would significantly weaken their stance on all other regulatory matters. I half wonder if the reason they haven't reclassified yet is to hold that threat over the telecoms to make them play nice.
I'm asking out of curiousity.