Delete all contacts labeled "All on my Mac" from Contacts (desktop)?

jinet,

If your intention is to use iCloud Contacts, there is no need to retain "On My Mac" Contacts.

Additionally, if you have confirmed that iCloud contains all of your desired contacts, be sure to Archive your iCloud Contacts before you delete the On My Mac Contacts.

Be aware that if you delete an iCloud contact it will be removed from all of your devices.

If you are not comfortable deleting all of the On My Mac contacts at once, delete one or two, and confirm that those contacts remain in iCloud Contacts.

Get help using iCloud Contacts, Calendars, or Reminders - Apple Support should also be consulted if you have any doubts.

jinet wrote:

THanks. I'll perform the archive first (though Time Machine should already have this data?). But still, how do you delete the contacts from a local drive? And: if you delete these, it sounds like this will delete the iCloud data too; will it?

It is always better to have multiple sources of backups.

Open Contacts, and make sure that you select View>Show Groups. Then the left sidebar will display all sources of data used by your Contacts Application. There should be an "On My Mac" Group. If you delete contacts from that group, they will not be deleted from iCloud.