Set expiry limit for blob
We don't currently have automatic expiration for blob storage. To your point you could use something like WebJobs to run a background task to delete files. If you have a large number of files that you create each day a simpler approach could just be to create a new container each day and store the blobs created each day in that container - then each day you just delete the container that is 31 days old. You could also do something similar with Tables whereby you create a new Table each day - and then delete the Table that is 31 days old.
I landed here from Google, so I'm leaving this for future readers. Microsoft currently has Blob Storage lifecycle management in public preview.