The grace of God is the reason that the Gospel is power.
God has things he requires of us, but they are things we cannot do in our flesh. Romans 7 is true.
In fact, the Epistle to Diognetus says the very purpose of Old Testament times was to convince us that we cannot attain to the kingdom of God by ourselves.
It's that last phrase I want you to catch. "that … we might through the power of God be made able."
Real grace from heaven will make us able to attain to the kingdom of heaven.
It's interesting to me to note that this is right after Titus 2:1-10, the passage this whole doctrine section rests on. The doctrine according to godliness depends upon the grace of God which produces godliness!
The grace of God is said in Romans to break the power of sin (6:14). It's said in Hebrews to help us in our time of need (4:16). It's said in 1 Peter to produce spiritual gifts for building each other up (4:11-12).
Grace is a marvelous thing.
Think about what we've said in this short section. Now, have we said enough to put some extra meaning in the words "for by grace are you saved through faith"?
Paul wasn't making a minor statement in Ephesians 2:8. He was not telling us that God would merely overlook sin.
Just three chapters later, in the same letter, he would tell us that immorality, uncleanness, and covetousness will cost us our inheritance in the kingdom of Christ and God (5:5). Sin will not be overlooked!
It was only two chapters later that he told us that if we learned about Jesus in truth (true doctrine), then we wouldn't continue to walk as the Gentiles do (4:17ff). Clearly, God's grace has nothing to do with his overlooking sin.
Paul specifically warns us not to be deceived about that (Eph. 5:6).
Twice (1 Cor. 6:9).
John, too (1 Jn. 3:7)
Grace is the power of God to salvation. If you are saved by the grace of God (and grace is only obtained by faith—Rom. 5:2; Eph. 2:8) then you are "his workmanship, created in Christ Jesus to do good works."
This is exactly the idea given in Titus 2 as well:
This is the grace of God according to the apostles.
The Law could not deliver us from our sin; only grace can.
Romans 7 describes the weakness of the Law. It was made weak by our flesh, which it could not overthrow. However, what the Law could not do, Paul says, God did.
He did it by sending his own Son in the likeness of sinful flesh, as an offering for sin, so that the righteous requirement of the Law might be fulfilled in us who walk by the Spirit.
May this understanding of the grace of God send you running to that grace for the salvation only it can bring.