"Lordship Salvation" is deceiving

From time to time I've listened to "Grace to You" with John MacArthur. We've brought up issues with him before, but I thought I'd give him a chance, & most of his messages I have no problem with. Today he started a series entitled "Examine Yourself", & some of his statements were true. In this message he said you have to come to salvation on Christ's terms, not your own, & there's no doubt about that. But he came out & said that believing in Christ is not enough to save you. If he was just thinking about how, "the demons believe & tremble", that can be backed up, but I think he was taking it farther than that. He said that true Christians live "righteously", which is true, except it sounded like he was implying that it's our own responsibility to live righteously - but we can't live righteously without the Holy Spirit! He was using the Sermon on the Mount as a pattern that Christians must live by, without saying that we can't live that in our own strength. I think because of when the Sermon on the Mount was preached - the context - it was like the Law, showing us that we don't meet those standards & need Christ to interceed. It's true that true Christians will bear the fruit of the Spirit, but that's the result of salvation, not the means of salvation. I guess my point is this: John MacArthur is preaching truth, but emphasizing the wrong things. He needs to better explain what the words "believe" & "righteousness" mean, because from the context of his sentences, one could get the wrong interpretation. The Law is a mirror to show us our sin, so we need that! But "not by works of righteousness which we have done, but according to His mercy He saved us..."