What does Romans 10:6 mean?
Moses wrote about a righteousness based on keeping the law (Leviticus 18:1–5). That's what Paul wrote in the previous verse. The problem with trying to achieve that righteousness is that nobody can keep the law. As fallible people, we're bound to sin and fall short of God's standard of perfection (Romans 3:10; 3:23). Those who try to earn salvation based on good deeds or following the law, are doomed (Romans 3:20).Now Paul describes a righteousness that is based on faith. Specifically, those with faith in Christ can achieve, through Christ's life and death on their behalf, a state of permanent righteousness before God. Now Paul explains this righteousness as if it were speaking in some way. It is offering a warning to Israel, and Paul quotes from Israel's own Scriptures to make the point.
First, Paul quotes the opening words of Deuteronomy 9:4–6: "Do not say in your heart." Though he doesn't quote the rest of the passage, Paul's Jewish readers would likely have understood the context. God was repeatedly telling Israel not to deceive themselves: they were not taking possession of the promised land because of their own righteousness. God called them a stubborn people. Instead, they would succeed in taking the land because it served God's purpose of judging the wicked nations of the region.
Paul's message to the Israel of his day is clear. They were seeking to achieve a righteousness of their own, which is a futile attempt for sinful human beings. That's the wrong attitude, and the wrong way to approach our relationship to God.
Next, Paul begins to quote from Deuteronomy 30:12. He applies what God says to Israel, about receiving and obeying His commands, to their need now to put their faith in Christ. In Deuteronomy 30:11–14, God said the command He had given to Israel was not—is not—too hard for them. They should not ask "who will ascend into heaven" to find out this information. They already have the command in their mouths and hearts (Deuteronomy 30:14).
Now Paul applies this idea to Christ. Israel should not think that faith in Christ is too hard for them. They ought not expect some new person to go to heaven to find the Messiah. Paul writes in his context that this would be a futile attempt to bring Christ down when He has already come down and walked among them (Romans 10:8).