Sergey, I must be missing something.

I have added:
ALTER TABLE [dbo].[mytable] ADD CONSTRAINT [DF_mytable_notes] DEFAULT ('') FOR [notes]

The notes fields is a TEXT fieldtype. Using SQL Server 2008.

I am still getting the same error message:
No data was provided for column 'notes' on table 'mytable', and this column cannot contain NULL values...

When I view the table in SQL Server Management Studio Designer the field constraint is in place. Default Value or Binding = ('')

What am I doing wrong?