After deleting a large file, how long does it take `df` to pick up the change?

It sounds like the file is still open by some process. You'll need to restart that service for the disk space to be freed.

If the filesystem was out of space you could be running into the reserved space on the filesystem. The ext2/3/4 filesystems have some reserved space set aside for root. By default this is 5%. So if it was full and 2.3GB is less than 5% of the space on the drive the filesystem will still appear to be full.

In this situation you have two choices. To continue to free up space to the point that you have usable free space or modify the amount of space the filesystem has reserved. To modify the amount of reserved space use the tune2fs -m 0 /dev/sda1 replacing the 0 with the percentage of reserved space you wish to have and /dev/sda1 with the appropriate device.

See the accepted answer to this question for more details.