Are you doing this from within the administration component, and are you drag and dropping the user or right click then Add/Remove Groups?
What group type are you trying to add the user to?
The tps_user_groups table doesn't contain any free text fields so its not the link itself which would be complaining, however I think we you map the user it tries to update and save the user record.
Are there any text fields on the user record that seem longer than other users?
As Julian said if this is an import then you can check your text field lengths using Business Object Desinger and then truncate fields as part of an import schedule.