If you use a TA site that I can't mention, you sort per night you can find some deals and often they are repos/TA/TPs or just super long:
Oceania Rome to Miami, 15 nighter, balcony, BEFORE fees and taxes $3,199/pp
Azamara Miami to Miami, 14 nighter, balcony, BEFORE fees and taxes $3,993/pp
SilverSeas, Portugal to FLL, 14 nighter, balcony, BEFORE fees and taxes $4,650/pp