Can't sync Contacts between iCloud and iPhone

I can't sync Contacts from iCloud to iPhone (5s; iOS 8.2). But Mail syncs fine.

I can't delete my iPhone's iCloud account, because "Verification Failed. There was an error connecting to iCloud." Basically, iCloud refuses to recognize my (legitimate) Apple ID Password.

Settings > Mail, Contacts, Calendars > iCloud… produces the "Verification Failed" error.

Settings > Mail, Contacts, Calendars > Mail > Default Account… is set to "iCloud".

Settings > Mail, Contacts, Calendars > Contacts… does not offer an option to Delete, or to Add, Contacts.

Settings > Mail, Contacts, Calendars > Fetch New Data… is set to "Push > iCloud".

Any ideas for a solution? TIA.