Is the placing of one's faith in Christ for salvation, a work? - Can I produce faith on my own? How does the Bible answer that question?
You have asked for a biblical answer, and there are certainly different positions on this. Some who believe that works are essential for salvation will refer to belief/faith as a work. Indeed, if faith can be classified as a work, then requiring additional works for salvation seems more reasonable. Yet, there appears to be good reason to distinguish faith from works.
Ephesians 2:8-9 is, of course, a key passage:
For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, 9 not a result of works, so that no one may boast. Ephesians 2:8-9 ESV
Salvation comes through faith, but salvation is not our own doing, but a gift of God. Salvation is not a result of works (but of faith). Faith, then, is distinguished from works.
(Some assert that faith is the gift of God, "this" does not match "faith" in gender, so that doesn't really fit. It would be like saying, "my brother and his wife came over, and he got a new job--you would know I am speaking about my brother getting a new job because of the gender agreement)
There are quite a few other passages that demonstrate salvation is by faith, but not by works:
But now the righteousness of God has been manifested apart from the law, although the Law and the Prophets bear witness to it— 22 the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction: 23 for all have sinned and fall short of the glory of God... Romans 3:21-23 ESV
For we hold that one is justified by faith apart from works of the law. Romans 3:28 ESV
16 “For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life... 18 Whoever believes in him is not condemned, but whoever does not believe is condemned already, because he has not believed in the name of the only Son of God. John 3:16, 18 ESV
We ourselves are Jews by birth and not Gentile sinners; 16 yet we know that a person is not justified by works of the law but through faith in Jesus Christ, so we also have believed in Christ Jesus, in order to be justified by faith in Christ and not by works of the law, because by works of the law no one will be justified. Galatians 2:15-16 ESV
I was reading in Romans last night and came across this verse that specifically distinguishes works from faith:
And to the one who does not work but believes in him who justifies the ungodly, his faith is counted as righteousness. Romans 4:5 ESV
Paul speaks of the one who does not work, but believes--that person's faith is counted as righteousness. Thus, faith is not a work, but is contrasted with works.
The deepest part of the man's being is his spirit, and if you salvage that deep then you have saved a man, and that is the only place needs light and when that light comes in or a perception of it then such a man becomes saved, and this is only done through the acceptance of the death on the cross as well as the acceptance of the holy spirit and resurrection from the dead.
Its the only way, then works is the manifestation of the working power of the recreated spirit of man. be blessed all of you.
Faith is a gift from God. Can you say that you mustered faith?
The issue is deeper than the simple, "you gotta have faith." (implying that the faith you have is from you and not itself a gift) Proper Biblical interpretation comes only from allowing the less clear passages be defined by those which are more clear. With this being the case, ask what a dead person does? Answer: nothing! (with the possible exception of rot) Scripture repeatedly declares that our spirit (or our true being) is DEAD. *see valley of the dry bones in OT if you wish to see an example other than what is found in the NT. God does not change.
We are dead in our trespasses and sins. We aren't sick or drowning or lame...we are dead. Apart from God's specific intervention, acting on YOU (not a broad stroke of man in general) you are dead. Further, you are not guiltless. Your nature (spirit) is guilty of transgressing God's law. Again, God does not change. Yes, we now have grace but it is God who metes out His grace. He doesn't have a grace convenience store where we can run in and get some grace. He gives it freely. Freely does not mean "to all." Freely means that He gives it without charge.
Think this is harsh? Read Romans. Who are you to question God. He makes some a vessel of honor and some a vessel of dishonor. Until you reach a point that you understand that believers exist because of God's faith and His mercy and that the very fires of hell declare His righteousness, you don't have a Biblical understanding of God.