Can we accept as a general statement the following: "You are saved through the blood of Jesus, and through His blood only. Because your salvation is not based on your performance, it is based on what Jesus did 2000 years ago on the cross"?
I also would like to bring up Matthew 19:25-26 and Mark 10:26-27: "This amazed his disciples more than ever. They asked each other, who then, can be saved? Jesus looked at them and said it's impossible for people to save themselves, but it's not impossible for God to save them."
Now in essence I agree with both the general statement and what Matthew and Mark say, but I would like to challenge the validity of especially what Jesus said, and I reiterate "it's impossible for people to save themselves" with two Bible verses: Mark 11:24 and Matthew 21:22, and suggest that through the power of prayer that it may be possible for a person to save themselves by prayer. After all, it is Jesus who said, "Therefore I tell you, whatever you ask for in prayer, believe that you have received it, and it will be yours."
My two questions: Can a person praying for their salvation, receive salvation? We have Jesus saying what can be deemed as "opposing" messages. On one side Jesus is saying it's impossible for people to save themselves, and on the other side, we have Jesus saying, "pray and believe that you will be saved," and you will be. Clearly that means a person can save themselves. What's right and what's wrong?
(Now I realise that I have paraphrased Mark 11:24 and replaced "whatever you ask" with "wanting to be saved")
We have all placed ourselves into a debt which we cannot repay. You see, all of us have sinned (Romans 3:9-20, 23), and those sins have justly earned us the penalty of death (Romans 6:23). Who then can cover our debt? How can we extract ourselves from the bondage into which we have sold our souls (Romans 6:16, 19-21)? You see the redemption of a man's soul is costly. "No man can by any means redeem his brother or give to God a ransom for him – for the redemption of his soul is costly, and he should cease trying forever – that he should live on eternally, that he should not undergo decay." (Psalms 49:7-9).
Think about it. We have already sold our souls to the devil, so we cannot buy ourselves back. What else do we possess that we could possibly offer in exchange for our souls? Money and worldly possessions cannot follow us across the river of death (Psalms 49:16-17). Besides all that is in the world already belongs to the Almighty Creator. Do you see the mess men get themselves into when they sell themselves into sin?
This is why Jesus said that men, by themselves, cannot achieve salvation. "When the disciples heard this, they were very astonished and said, "Then who can be saved?"And looking at them Jesus said to them, "With people this is impossible, but with God all things are possible"" (Matthew 19:25-26). But where we are powerless, God is able to redeem (Psalms 49:15). It is one of the reasons that it was critical that Jesus was sinless. Since Jesus wasn't trapped in sin, he could make the payment required for those lost in sin.
While man cannot save himself, it is a mistake to conclude that God did all the effort and man only has to sit back and enjoy the fruit of Christ's labor. God put requirements on salvation that separates those who are deserving of salvation from those who prefer to remain in sin. Those requirements don't earn a person salvation -- that is, they do not force God to say a man must be saved. Man's best efforts remain inadequate. But without requirements, then God would be unjust because everyone would be saved, whether they gave up sin or remained in it.
You recognize the need for a requirement because you put prayer as the condition on receiving salvation. Prayer by itself would never save anyone. If we use the slavery example, all the begging a slave may make would not be enough to win his freedom. It would still require someone else to accept the request and grant the freedom. Therefore, your own example doesn't prove that men can save themselves by prayer alone.
A better point then, is whether God placed prayer as a condition before He grants salvation. It is here that your example fails. God doesn't state that men are to pray for salvation. The passages you gave were to the disciples, who were already saved, to ask according Jesus' will and their prayer would be answered. "This is the confidence which we have before Him, that, if we ask anything according to His will, He hears us" (I John 5:14). As an example, Cornelius prayed (Acts 10:1-2), but he still had to send for Peter to teach him God's word (Acts 10:22) and he still had to be baptized (Acts 10:47-48).
So why reject what God has plainly stated? We can read the Scriptures, find the passages regarding salvation and see what is connected to salvation. Then you learn that there was effort made by God to rescue mankind and requirements placed on men to accept the efforts of God on their behalf. See: What Saves a Person?