The larger context of Ro 9-11 is concerned to answer the question, "Is God righteous in the way He has dealt with the Jews?" The entire passage is a "theodicy" or justification of God against the charge that He had not given Israel sufficient resources to believe (see Ro 9:6, the key to the entire passage).
Ro 9 answers, "Yes, God is right because He is sovereign." Of course, the proof Paul cites for Divine sovereignty is the doctrine of election. Ro 10 continues the vindication (or justification) of God by driving home the point that He had given the Jews every conceivable opportunity for repentance, but still they, as a nation (or generally speaking), rejected their own Messiah. Ro 11 adds to this discussion a note of hope in a two-fold sense: (1) Though Israel in general refused to acknowledge their Messiah, yet a remnant of believing Jews was preserved by God's grace; (2) Though Israel is presently cut off and in a state of judicial blindness, yet God reserves the right to "graft them in again".
In lieu of this larger context, then, Ro 10 develops the thought of God's rightness in judging Israel. He is just to cut them off from gospel blessings in lieu of their unbelief. This chapter affirms that unbelief is not so much a matter of hesitancy or reluctance to embrace a fact as it is a matter of refusal to accept the evidence.
The entire epistle of the Romans is written in a "dialectical" literary style. Dialectic is the practice of debating oneself, a popular device among authors. If a writer wanted to expose the fallacy of a certain position, for example, he might pretend to hold a debate between two contrary positions. He would first advance the contrary position and then offer counter arguments to disprove each point. That Paul employs the device of dialectal rhetoric in Ro 10 is clear from his use of the phrase "But I say" in Ro 10:18 and Ro 10:19 (see the same formula in Ro 6:1,15; 7:13; 8:31-39; 9:14,19; 11:1).
So, the overall question in Ro 10 is, "Is God righteous in dealing so severely with Israel?" He proceeds to tackle that question by giving the Jews answer (as he envisions it), "No, He is not righteous for we have not had sufficient opportunity to hear and embrace Christ as the promised Messiah. We need someone to ascend into heaven or descend into the deep before we can believe." Paul responds, "You don’t need to witness an external miracle. The child of God already has an inward witness. The word is nigh thee, in your heart and in your mouth--the evidence you need is already there." In Ro 10:14, he anticipates their second argument, namely, "We cannot embrace Him unless some preacher come to tell us about Him." Paul retorts, "You have already heard, but you didn't obey" (Ro 10:16). “The problem, in other words, is not with God and His provision for you. He has in fact given you both an internal and an external witness. The problem is in yourselves and the obstinate resistance to the evidence [i.e. unbelief].”
Paul's closing argument in this "trial of God" is in Ro 10:18-19. "But I say, have they not heard? Yes...But I say, did not Israel know...?" The implied answer is again "yes, they did know, but they refused to accept the evidence--i.e. unbelief." Ro 10:20 further accuses them by saying that one of their own prophets predicted that the Gentiles would embrace the Messiah that the Jews rejected. And Ro 10:21 concludes the debate by ultimately vindicating God, "All day long have I stretched forth my hands to a disobedient and gainsaying people" (doesn't sound like an effectual call, does it :-)). In other words, Israel has no case at all. The Lord had gone above and beyond the call of duty, so to speak, in the way He dealt with them, but they spurned his advances and rejected his revelation. Therefore, He is justified to cut them off in unbelief.
That is the case against Israel. Paul, nonetheless, has a great passion for their "salvation" to Gospel blessings (Ro 10:1-4) and holds out hope for their restoration because of the remnant that God had graciously preserved (Ro 11:1).