Yes, I agree, knowing that we will die one day, that our lives on earth will come to an end does give us a sense of urgency. It also helps us to treasure our relationships here much more.
But I believe in what Jesus says about eternal life, that whoever believes in him shall not parish but have eternal life. This doesn't mean that we won't die, but that our spirit and soul lives eternally and when we believe in him we will be resurrected one day with renewed physical bodies, and live in a restored new heavens and earth free from corruption, sin and decay, where there will be no more death, sickness or tears. I believe this because I have experienced the presence of God and his reality, and that there is sufficient historical evidence for the resurrection of Jesus from the dead, with over 500 eye witnesses to this event which has changed our world and history forever. So I believe in what Jesus has promised.