Adam and Eve were not supposed to die. In the beginning, God blessed them in such a way that they would never get sick, never suffer and never grow old. Paragraph 376 of the Catechism of the Catholic Church says, "As long as he remained in the divine intimacy, man would not have to suffer or die."
God's plan for Adam and Eve, as well for all their children until the end of time, was to live a full life, grow in virtue and eventually be drawn up to Heaven without any suffering whatsoever. We know, of course, they sinned and lost this blessing for everyone, but that's another story.
Along with the gift of immortality, Adam and Eve started out with sanctifying grace, but they also had two more special blessings. The first was the gift of knowledge called infused science. This was like an owner's manual of life that God download into their brains so they would know how to live and what to teach their children about life in the world. An example of this knowledge is found in Genesis 2:19 where Adam names the animals. Names back then meant something specific about the thing named. Their brains too weren't sluggish and slow to learn as the minds of people are today.
The next blessing gave their emotions the ability to be completely balanced and always reasonable. For instance, they didn't have unusual cravings, fly off the handle, or want to sleep all day. The Catechism says our first parents had an inner harmony, called the gift of integrity, that allowed them to be at peace with one another, with God and with nature.
Even nature back then was blessed and at their service. This was shown in Genesis 2:15 where God placed them "into the paradise of pleasure to dress it and to keep it." After they fell from grace this blessing would be lost and the earth would begin to yield "thorns and thistles."
Discover the blessings bestowed on our first parents in season one of Church Militant's Premium show Armor of God—The Creation and Fall of Man.