In this passage, Paul is discussing what the righteousness of faith says to the world - Jews and Gentiles alike. In verse 9, Paul begins to discuss what is included in coming to Christ. I've found verses 9 and 10 to be somewhat confusing because Paul seems to distinguish between confession and believing and says that we're justified when we believe and then we're saved when we confess. However, in the context, these two words (justify and saved) are basically synonymous. According to R.C. Sproul, Paul changes the order of confession and believing in 9 and 10 to show the absolute necessity there is in linking confession with belief.
Let's focus on Romans 10:9-14: "because, if you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved. For with the heart one believes and is justified, and with the mouth one confesses and is saved. For the Scripture says, "Everyone who believes in him will not be put to shame." For there is no distinction between Jew and Greek; the same Lord is Lord of all, bestowing his riches on all who call on him. For "everyone who calls on the name of the Lord will be saved." But how are they to call on him in whom they have not believed?..."
A question still remains - what about this "calling" that's mentioned in verses 12-14 (after which confession is not even mentioned)? How does calling relate to a believer's coming to Christ? Obviously, Paul "assumes that one must call upon the name of the Lord to be saved" (Systematic Theology, Grudem, p. 116). However, how does Paul separate "calling" and "confession" while still maintaining "sola fide?"
Here is where my studies have led me thus far. To quote Grudem again,
"Jesus speaks of 'coming to him' in several places. He says, 'All that the Father gives me will come ot me; and him who comes to me I will not cast out' (John 6:37). He also says, 'If any one thirst, let him come to me and drink" (John 7:37).... In these passages we have the idea of coming to Christ and asking for acceptance, for living water to drink, and for rest and instruction. All of these give an intensely personal picture of what is involved in saving faith" (Systematic Theology, p. 711).I will try to pull his quote together and support it with biblical insight. As we all know, the basic definition of faith is trust in or reliance/dependence on someone or some thing. But, what does that entail? And, again, how do we maintain "sola fide?"
"'J.I. Packer presents [faith] as an 'appropriating instrument, an empty hand outstretched to receive the free gift of God's righteousness in Christ'" (Christ the Lord, p. 103). Packer and Grudem describe faith as something which goes outside of the person to another for salvation. And, faith includes "calling" or "asking" for forgiveness from the individual it goes to. This is even obvious in passages like Joel 2, Romans 10:13, Acts 2:32, etc.
So, how is "calling" and "asking" not a work? The answer is because these two things are an outflow of what true faith is at it's core. If we truly posess faith, we must be depending on Jesus. And, that dependence looks like going to Him for salvation. As John Piper says, "Coming to God for salvation means believing on Christ in your heart for all that he has done for you, and then giving expression to that with your mouth by confessing him and calling on him as Lord" (www.desiringgod.org).
What I love about Piper's definition is that he puts this all together (using Romans 10). He states that confessing and calling are merely an expression of your faith. So, that is not a work. It's merely the natural verbalization of what you believe.
What can be said of those who "don't know when they were saved?" Again, it's the heart attitude that matters. The heart attitude is one that goes to Christ, and depends on Him by calling to Him for salvation.
With all of this, I will close with Calvin's quote on this passage:
"...the apostle, in order to show that true faith cannot be indifferent about calling upon God, has laid down this order: just as faith is born from the gospel, so through it our hearts are trained to call upon God's name [Rom. 10:14-17]" (Calvin: Institutes of the Christian Religion 2, ed. John T. McNeill, p. 850).