I think the objection is not that he's a commoner, but that he's not a WORLDLY person with a great education. Sylvia, the Queen, was a commoner, but spoke/speaks about 6 languages, has amazing social skills, and adapted immediately to her duties. She comes from a wealthy family and was used to a more aristocratic lifestyle.
My guess is that if Victoria wants to marry Daniel, they'll let her, provided he undergoes the requisite "training". The King kinda likes him....