Some have taken the story told by Luke, of the Savior telling the criminal on the cross next to him "To day shalt thou be with me in paradise", as evidence that salvation can be obtained while on the deathbed. Modern day revelation gives us further insight into the concept of deathbed repentance.
- “The infidel will grasp at every straw for help until death stares him in the face, and then his infidelity takes its flight, for the realities of the eternal world are resting upon him in mighty power; and when every earthly support and prop fails him, he then sensibly feels the eternal truths of the immortality of the soul. We should take warning and not wait for the death-bed to repent; as we see the infant taken away by death, so may the youth and middle aged, as well as the infant be suddenly called into eternity. Let this, then, prove as a warning to all not to procrastinate repentance, or wait till a death-bed, for it is the will of God that man should repent and serve Him in health, and in the strength and power of his mind, in order to secure His blessing, and not wait until he is called to die.”
Additionally, President Spencer W. Kimball wrote in his book The Miracle of Forgiveness;
- “It is true that the great principle of repentance is always available, but for the wicked and rebellious there are serious reservations to this statement. For instance, sin is intensely habit-forming and sometimes moves men to the tragic point of no return. Without repentance there can be no forgiveness, and without forgiveness all the blessings of eternity hang in jeopardy. As the transgressor moves deeper and deeper in his sin, and the error is entrenched more deeply and the will to change is weakened, it becomes increasingly near-hopeless, and he skids down and down until either he does not want to climb back or he has lost the power to do so” 
These teachings suggest that while the Savior is capable of saving anyone, even on their deathbed, waiting to repent until the deathbed is an extraordinarily bad and idea contrary to the intent of the Savior and the Plan of Salvation.