I believe it is safe to say that, if asked "Do you want the lost to be saved," every born again believer would answer in the affirmative. That is, every Christian would say they honestly want all those who are not children of God by faith in Jesus Christ alone, to turn to Him and place their total trust in Him. Many believers are also aware that although men view some sinners as being more deserving of God's judgment than others, sin is sin, and "the wages of sin is death" (Rom. 6:23). But unfortunately, not all of God's children have God's attitude when it comes to child molesters, rapists, murders, etc.; God does not want any to perish, but that every single lost person would be saved (2 Pet. 3:9). So, when it comes right down to it, many believers do not actually want "everyone to be saved."
Many of us have our own list of "unpardonable" sins, but to God, there is only one unpardonable sin. In Matthew 12:31-32, and in Mark 3:28-29, Jesus told those who rejected the Holy Spirit's witness to His identity (Matt. 12:22-23; Mk. 3:22), that by saying the evidence was the work of the devil, they had blasphemed the Holy Spirit, and they were guilty of the only sin God would not pardon. When a person rejects the Holy Spirit's conviction that they should put their faith in Jesus, they are, for all practical purposes, calling His witness a lie; and Satan is the father of lies (Jn. 8:44; 16:8-11).
Unlike some of my brethren, I do not believe the unpardonable sin was limited to the rejection of the miracles of Jesus while He was on earth. Jesus still works miracles, and the Holy Spirit still brings conviction. Rejection of the Holy Spirit's work today, just as it was during the time of Jesus, is paramount to calling Him a liar. Jesus died for the sin of the whole world (Jn. 3:14-17; 1 Jn. 2:2). The Spirit attempts to convince each person of that truth. To reject Jesus is to blaspheme the Holy Spirit.
That being said, Christians are to preach the Gospel to "every creature" regardless of what they have done (Mk. 16:15). If we exclude those who are guilty of the most horrible sins, we are being disobedient to the Lord's command. If we do share the Gospel with them but do not really want them to be saved, God will deal with us like he did Jonah (Jon. 3:10 - 4:11). We need to love the "unlovable."
Another difficulty when praying for the lost is, who are they? Christians who are walking in the flesh cannot be distinguished from the lost (Rom. 7:1-25; 1 Cor. 3:1-3). And, even though Jesus said you can recognize "wolves" by their fruit (Matt. 7:16, 20), many religious unbelievers appear to produce the fruit of the Spirit (Gal. 5:22-23). It is almost impossible to know who is saved and who is not. The solution? Pray for the souls of every man. If you ask God to draw each one closer to Himself, you are praying for both, the brethren, and the lost (Eph. 6:18; 1 Tim. 2:4).