"I wonder if our obsession with longevity is really healthy?" - Christopher Buckley.
I think the Biblical answer is yes and no.
"He hath set the world (eternity) in their heart" (Ecclesiastes 3:11).
"What is your life? It is even a vapor, that appeareth for a little time, and then vanisheth away" (James 4:14).
It is a fool's game to emphasize quantity of earthly life rather than quality. We have no guarantee of threescore and ten, no guarantee of tomorrow, and no guarantee of even the next earthly moment. We have this moment, along with its great and looming issue: Am I living right now for the glory of God, the fulfillment of His will, and the furtherance of His eternal purpose in Christ Jesus? This is the quality of life to which born again believers in the Lord Jesus must devote themselves, and which makes our lives truly life. "To live is Christ" (Philippians 1:21).
This being said, it remains true that quantity of life is a valid consideration and hope. Eternity is in our hearts, that is, the longing for permanent consciousness and experience. God Himself set this sensibility within us, and through Christ makes possible an eternity of heavenly life with Him. Emphasis upon this longevity is a very healthy thing, and one which presses us toward the focus on the matter of quality in our earthly lives.
"Our light affliction, which is but for a moment, worketh for us a far more exceeding and eternal weight of glory; while we look not at the things which are seen, but at the things which are not seen: for the things which are seen are temporal; but the things which are not seen are eternal" (II Corinthians 4:17-18).
Every human being will exist forever. But not every human being will live forever. The Lord Jesus Christ is the issue. "I am... the life" He declared, the life for this day, this lifetime, and eternity to come (John 14:6). The quality of our lives is determined by how consistently we know, trust, love, obey and communicate Him to our world in example and word. Quantity, the real quantity of eternal life, flows from emphasizing the quality of God's devotion to us, and ours to Him. Our "obsession with longevity" is therefore very healthy as long as the life we seek is heavenly rather than earthly.
"If ye then be risen with Christ, seek those things which are above, where Christ sitteth on the right hand of God. Set your affection on things above, not on things on the earth. For ye are dead, and your life is hid with Christ in God."