Did your INR STAY low even after you increased the dosage of Warfarin? Did you not respond to increased dosages?
The liver is a key organ in the process of creating some of the factors responsible for coagulation. Warfarin is what they call a Vitamin K agonist - meaning that it looks to the body as if it's Vitamin K, the body attempts to use it to create coagulants, but these coagulating agents aren't manufactured.
I personally don't know if a failing liver would INCREASE or DECREASE your INR. (FWIW - there was a CSI show a couple weeks ago where a hepatotoxin (liver poison) was mixed with a drink, causing liver failure, and the people died from internal hemorrhaging -- exactly the opposite of the low INR that you're reporting).
If your INR was low, and didn't respond to steadily increased doses of Warfarin, I'd certainly talk to your doctor. If it was low, and you didn't change the dosage, and it fluctuated between 1.9 and 2.7, as you reported, these changes are probably normal. I think that all of us who've tested have had interesting fluctuations that were hard to explain -- it could just be that, in your case, whoever was managing your dosing may have just not been giving you enough to get you into the 2.5 range.