Paul goes through Isaiah, Deuteronomy, and the Psalms in this passage to show that what he is explaining is not new territory.
At first, he begins with an intensely simple argument. God uses means to reach people. He sends messengers preaching the gospel that our God reigns. The picture is that of a messenger coming back from a battlefield proclaiming victory in a battle. How exciting and blessed is the message. Paul is not exalting the messenger but the message that they bring. Their feet are beautiful because of the wondrous victory they proclaim.
So, since the message of that victory is to be given to people so that they might be saved, did Israel not hear it? Paul brings back his original argument from Romans 1 through Psalm 19:4. In Psalm 19, even the heavens proclaim the glory of God. But here Paul takes that language and applies it to the gospel going out to all people, to Israel first, through Christ and the Apostles, and also to the Gentiles.
Paul recalls Deuteronomy 32:21, reminding Israel that if they made God jealous with those that are not gods, God would make them jealous with those that are not a people. Here Paul is speaking of the Gentiles.
But God has not abandoned them, or us. “All day long” He holds out His hands to a disobedient and contrary people.
Faith comes then from hearing the word of Christ. Yet hearing the gospel demands a response. If we have not obeyed His word and submitted to His rule, then we are called to. If we have, then we are to be in the work of helping others hear that word of Christ, as we imitate our Father, all day long holding out the gospel to them. Not because we are capable of producing salvation, but because He is worthy.
-steve