Paul’s logic is patently clear: Israel did not obtain righteousness (as a status before God) while the non-covenant people, the Gentiles, did obtain righteousness. Paul clarifies why “Israel” did not get it and why the Gentiles did:
Actually, Paul’s language is not quite what I said: Israel, Paul says, did not obtain “the Law” because Israel was pursuing a “law of righteousness.” I take “Law” here to mean the status of having obeyed the Torah.
Israel does not get righteousness, Paul says, because they cling to the Torah in the wrong way; the Gentiles get it because they have faith (Rom. 9:32). Israel clings to the Torah with “works” (9:33).
Righteousness comes not by works but through the new covenant (Rom. 10:6-9).
What is in Paul’s mind by “works” here? Wright contends it could refer to the list of commandments but more likely refers to the boundary-marking characteristic in Jewish privilege.
What is sometimes missed in this passage is that Paul blames Israel for not responding to the Messiah and that is why they fail to obtain righteousness. Rom 9:33 is about the Stumbling Stone in whom there is righteousness and over whom Israel has stumbled and fallen. If one trusts in this Stumbling Stone, one will not be put to shame.