The Execute method of job definition Microsoft.Office.Server.Search.Administration.IndexingScheduleJobDefinition - threw an exception.

Error Details:
The Execute method of job definition Microsoft.Office.Server.Search.Administration.IndexingScheduleJobDefinition - threw an exception. More information is included below.
Solution Details:

Step 1:
stsadm -o osearch -action stop

Warning: The Office SharePoint Server Search service that was enabled on this server will uninstall and all index files for all SSPs will be deleted. Are you sure you want to permanently delete all data in the index for all SSPs? [y/n]

NOTE: Only do this if you have not crawled / indexed content that cannot be re-indexed. If this is the case, then you open a support ticket with MSFT and work through it. Otherwise, hit Y

Step 2:
Now issue: stsadm -o osearch -action start -role index
You may receive the errror 'start' action failed. Additional information: the handle is invalid. Wait 30-60 secs and re-issue the command. It should go through fine.

Step 3:
Open Central Admin - select your SSP
Check / validate your search service configuration.