Scripture seems to support that "believing" in Jesus is necessary to receive eternal life.
John 3:16 - For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
John 6:47 - Verily, verily, I say unto you, He that believeth on me hath everlasting life.
Acts 16:31 - And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.
John 5:24 - Verily, verily, I say unto you, He that heareth my word, and believeth on him that sent me, hath everlasting life, and shall not come into condemnation; but is passed from death unto life.
John 14:6 - Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me.
Romans 10:9 - That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.
John 3:36 - He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him.
John 8:24 - I said therefore unto you, that ye shall die in your sins: for if ye believe not that I am he, ye shall die in your sins.