Jimmy Duck overhears stuff

Sometimes you hear one side of a phone conversation and what you hear is so stupid it bears repeating. Spacey spent a good 20 minutes on the phone with somebody today and this is part of what we heard.

"If you gave me the correct year, January 2nd and January 3rd are only a day apart."

Taking this statement to it's logical conclusion, Spacey must think that in some years January 2nd and January 3rd aren't just one day apart. Is there some year when there is a January 2.5, 2.6666, 2.8, etc?

Tell me more about this magical January.