If the error message (There's not enough space) is correct, as odd as it sounds, it is fully possible. The issue is this; TimeMachine backs up files that have changed or that are new since the last time the computer was connected to the drive. If it has been a long time since your MBAir was last connected, or, if you've made a big change to the MBA (like upgraded a program or the operating system) that would require a lot of space. Meanwhile, your MBPro might not have any major changes (or its major changes were backed up first taking up all the space).
TimeMachine should delete old backups to create enough space but there are two limitations. First, you have 2 computers backed up on the drive and I think TM will only delete the old backups of the computer it is currently backing up. I don't think it will touch old backups of the MBP to make space for the MBA. Second, I know it will only delete files that are duplicated. TimeMachine, by design, must leave everything that is needed to restore the computer as it was the last time it was backed up successfully. Sometimes TM just cannot delete enough space to fit the new backup.