Rebuilding the index will be fully logged in the transaction log. You could bring down your whole database server if you dont get this right.

Is the reason you are rebuilding related to performance issues or just doing a regular maintenance?

are you using sort_in_tempdb='ON', this may help in your case depending on where you tempdb is located and how much free disk space you have.

I'd also suggest you look at your t-log backup stragey and considering changing to backing up every 15 minutes.