Yes, it is possible to get a blood clot when you are on warfarin. I have Factor V Leiden, and have had 3 blood clots. When I had my 3rd clot, I was already taking warfarin. We were trying to keep my Pro Times at 2.5 to 3, so now we upped it to 3 to 3.5, and it is a constant battle to keep it in that range.