DO NOT ANSWER THAT QUESTION !!!
If you received this twice this means you have two problems.
1. you are running out of space on a LUN - this is very dangerous and can cost you nerves and valuable data in a good outcome and the whole LUN when you act in a hurry
2. you have a bug in administration setup
When you see any signs of a risk that a LUN may run out of space you MUST ACT.
Ok - that had to be said 
If you have not pushed the button yet - do this:
Find VMs that are not running right now and move them elsewhere to a different datastore - do not delete anything too quickly - I have seen to many bad mistakes in such a scenario ...
Free up some space - how much ?
I would say give as much space as 2 x size of latest snapshot of the VM that warns + 2 x vRAM of the VM that warns.
Power off other non essential VMs
Try to calm down other running VMs to reduce any diskoperations.
Do not suspend other VMs
Once that is done try the RETRY option and cross your fingers.
Often the damage is already done at this point.
If that still fails do NOT answer again - instead free up more space.
Hopefully you can get out of it now without needing to discard the current state.
Once you are running again - consolidate snapshots. Do not use SnapshotManager to consolidate large snapshots !!! - use vmkfstools instead.
If the VM is damaged it may not start at all or start with an outdated state.
Now do not start the VM again but create a backup of all vmware.logs, all vmdk descriptorfiles, the vmsd and the vmx-file.
Do not assign vmdks to other VMs before you are sure there is no way to fix the VM.
If you have to get data out of vmdks - mount them as non-persistant and use a LiveCD
.Post details if you run into this.
About the administration ...
If ou run vRanger, VEEAM or similar backuptools against VMs that you regard as "mission critical" you NEED a functional warning system when snapshot chains are getting out of control.
Install vcheck or something like that - receive your daily email and read it
If vRanger, VEEAM and friends fail to clean up snapshots they very likely mess up the vmsd file first.
Next snapshotmanager does not display snapshots - the problems no longer looks serious and during the next weeks you will get more and more snapshots until there is no way to consolidate them safely while the VM is running. A few days or hours later datastore fills up and the data of the last months is lost.
Does not matter - lets restore last snapshot ... oops - last good is months old ....
You do not want to experience this yourself ...
Ulli