Liverpool have a fixture againts Leicester on 27th December and two fixtures against Spurs and Man U in January. Apart from them, I don't find any major hurdles.
You sure about that? Bookies seem to think otherwise. Check out the odds for the league cup game vs Aston Villa next Tuesday:
from PinnacleLiverpool to WIN @6.7!!?? LOL

Let's see which one of you can figure out the reason for such strange odds (without having to resort to Google of couse, i'm watching you!!)
Its because they are playing in that club world championship, I think. The first team squad wont even be in the country to play Aston Villa. Be some kind of young kids playing.