You can obey news if the news story contains instructions from the relevant authorities. The Good News reveals that Jesus has full authority. As Savior, He gives salvation as a free gift (Romans 3:24; 6:23). As Lord, He gives on His terms, not ours.
His terms include obedience to the Gospel by sharing in the Gospel event. Romans 5 and 6 make this clear. Romans 5 emphasizes faith in Christ, including the grace given to us by the death and resurrection of Christ. Then Romans 6 shows how we enter Christ, joining Him in the Gospel event—His death, burial and resurrection.
Do you not know that all of us who have been baptized into Christ Jesus were baptized into His death? We were buried therefore with Him by baptism into death, in order that, just as Christ was raised from the dead by the glory of the Father, we too might walk in newness of life (Romans 6:3-4).
… having been buried with Him in baptism, in which you were also raised with Him through faith in the powerful working of God, who raised Him from the dead (Colossians 2:12).
We must die with Christ and rise to new life with Him. And the Lord Himself has chosen for that to take place in baptism. That is where we first “obey the Gospel.”