Possible Clues:

• One could never be happy so to break the rig over the First Lady
• Suffer intense sorrow
• It's enough to break the rig to get the girl to mourn for it (6)
• One is not glad that this sounds like a bit or armour
• What one may do in the morning, by the sound of it
• Deeply regret the rig-out first lady has on!
• Keen follower of Anne, the first lady
• Feel the pain
• Would a GI ever sound like this in the morning?
• The First Lady is mourning under the broken rig