What do you think that “confess with your mouth the Lord Jesus” means?
St. Paul specifies in the preceeding verse: "that is, the word of faith which we are preaching" (Rom 10:8). That refers to the deposit of the faith, the doctrine preached by the Apostles and perpetually guarded and passed on by the Church. The "confess with your mouth" St. Paul refers to is not just some kind of private statement (in one's bed at night), or in a conversation at the lunch table with friends that 'magically' makes one saved. It refers to the confession of the faith before the Church at the rite of initiation (baptism and confirmation/chrismation), through which one is incorporated into the Church. At that moment, one states that one believes and professes all that Church teaches, believes and proclaims to be revealed by God. Evangelicals and fundamentalists typically take the verse (Rom 10:9) completely out of its historical and ecclesial context, and turn it into 'sinner's prayer' theology.
-A8