Pity they didn’t look closer at the scriptures.
“The grace of faith, whereby the elect are enabled to believe to the saving of their souls,[1]” is justified by “[1] HEB 10:39 But we are not of them who draw back unto perdition; but of them that believe to the saving of the soul.”
Or as the passage reads in the ESV:
32But recall the former days when, after you were enlightened, you endured a hard struggle with sufferings, 33sometimes being publicly exposed to reproach and affliction, and sometimes being partners with those so treated. 34For you had compassion on those in prison, and you joyfully accepted the plundering of your property, since you knew that you yourselves had a better possession and an abiding one. 35Therefore do not throw away your confidence, which has a great reward. 36For you have need of endurance, so that when you have done the will of God you may receive what is promised. 37For,
“Yet a little while,
and the coming one will come and will not delay;
38 but my righteous one shall live by faith,
and if he shrinks back,
my soul has no pleasure in him.”
39But we are not of those who shrink back and are destroyed, but of those who have faith and preserve their souls.
The writer speaks to those who have believed, and encourages them to press on to the goal: “For you have need of endurance, so that when you have done the will of God you may receive what is promised.”
There is certainly nothing in that passage of God giving faith to his elect while denying it to everyone else.
“is the work of the Spirit of Christ in their hearts,[2]” is justified with:
[2] 2CO 4:13 We having the same spirit of faith, according as it is written, I believed, and therefore have I spoken; we also believe, and therefore speak.
EPH 1:17 That the God of our Lord Jesus Christ, the Father of glory, may give unto you the spirit of wisdom and revelation in the knowledge of him: 18 The eyes of your understanding being enlightened; that ye may know what is the hope of his calling, and what the riches of the glory of his inheritance in the saints, 19 And what is the exceeding greatness of his power to usward who believe, according to the working of his mighty power.
2:8 For by grace are ye saved through faith; and that not of yourselves: it is the gift of God.
2CO 4:13 reads, in context:
5For what we proclaim is not ourselves, but Jesus Christ as Lord, with ourselves as your servants for Jesus’ sake. 6For God, who said, “Let light shine out of darkness,” has shone in our hearts to give the light of the knowledge of the glory of God in the face of Jesus Christ.
7But we have this treasure in jars of clay, to show that the surpassing power belongs to God and not to us. 8We are afflicted in every way, but not crushed; perplexed, but not driven to despair; 9persecuted, but not forsaken; struck down, but not destroyed; 10 always carrying in the body the death of Jesus, so that the life of Jesus may also be manifested in our bodies. 11For we who live are always being given over to death for Jesus’ sake, so that the life of Jesus also may be manifested in our mortal flesh. 12So death is at work in us, but life in you.
13Since we have the same spirit of faith according to what has been written, “I believed, and so I spoke,” we also believe, and so we also speak, 14knowing that he who raised the Lord Jesus will raise us also with Jesus and bring us with you into his presence. 15For it is all for your sake, so that as grace extends to more and more people it may increase thanksgiving, to the glory of God.
Please note there is nothing in there about God giving faith to some, and denying it to others. In preaching the Gospel, they rely on the power of God in proclaiming it: “We are afflicted in every way, but not crushed; perplexed, but not driven to despair; 9persecuted, but not forsaken; struck down, but not destroyed; 10 always carrying in the body the death of Jesus, so that the life of Jesus may also be manifested in our bodies.”
As he wrote a few verses earlier, “We refuse to practice cunning or to tamper with God’s word, but by the open statement of the truth we would commend ourselves to everyone’s conscience in the sight of God.”
Ephesians 1:17 reads:
15For this reason, because I have heard of your faith in the Lord Jesus and your love toward all the saints, 16I do not cease to give thanks for you, remembering you in my prayers, 17that the God of our Lord Jesus Christ, the Father of glory, may give you a spirit of wisdom and of revelation in the knowledge of him, 18 having the eyes of your hearts enlightened, that you may know what is the hope to which he has called you, what are the riches of his glorious inheritance in the saints, 19and what is the immeasurable greatness of his power toward us who believe, according to the working of his great might 20that he worked in Christ when he raised him from the dead and seated him at his right hand in the heavenly places, 21 far above all rule and authority and power and dominion, and above every name that is named, not only in this age but also in the one to come. 22And he put all things under his feet and gave him as head over all things to the church, 23 which is his body, the fullness of him who fills all in all.
Again, note there is nothing about God giving faith to some and denying it to others, only that he wants the believers to understand “the hope to which he has called you, what are the riches of his glorious inheritance in the saints, 19and what is the immeasurable greatness of his power toward us who believe...”
Not “to those he chose by name before the world began”, but “toward us who believe”. Again, the onus is on us to believe, not for Him to give belief to us as a gift after first giving us life.
And of course, Ephesians 2:8 looks different in English than in the Greek, since the Greek makes it clear that the gift is NOT faith, but salvation.
I would suggest you get a copy of John MacArthur's excellent commentary on Hebrews. Hebrews is a book that must be read from the beginning to end. It is often completely misunderstood and quoted totally out of context with its intended purpose.
The book of Hebrews is an evangelistic message written to unconverted Jews who the writer was trying to lead to Christ. (Leave it to God to put an evangelistic call to the Jews in scripture.) The people who the writer is addressing his letter to are not people who "believed" but were close to believing. One might say they are the ones in Acts who said, "We will hear later."
John MacArthur's commentary is too lengthy (and is copyrighted) to be printed here. But here is a small excerpt from the commentary on the passage you cite:
The unbelieving Jews addressed in this passage were so attracted. They had not yet trusted in the gospel, but neither were they ashamed of it. They had been somewhat ridiculed, persecuted, and had property seized because of their association with Christians. But the association seemed worth the sacrifice, so that those problems had not yet caused them to turn away..."
These Jews were intellectually enlightened. ...But this is no substitute for faith itself.
There is certainly nothing in that passage of God giving faith to his elect
We've been around the block on this one before. Unless YOU want to claim that you generate your own faith, then it cannot be denied that God gives faith. The scriptures tell us that not all have faith, faith is given in measure and faith comes to us by hearing the word of God. So if God gives faith, then you are left with the inevitable conclusion that those who don't have faith, simply don't have it because God didn't give it to them.