Not really. Searching a bit finds many possible causes.
Is the server configured to use keys only? A bit difficult to use ssh-copy-id without being able to login without using keys or some other authentication...
Have you previously logged in via ssh with this client?
Have you previously setup keys for this client/user?
Are the permissions correct for the .ssh directory and private key?
What distribution / version and ssh version is running on the remote and client PCs?
Have you updated either system lately?
Have you tried copying the private key from another linux box for the same remote user to see if that works?
Adding -v to debug i.e. ssh -v
user@blah.blah.blah.blah -p blah might provide additional clues.
Something might be wrong with the authorized_keys file on the remote.