1. Calvinists don't believe that the work of the Spirit is always irresistible. But in the work of regeneration it is.Blammo said:
2. It says nothing about the work of the Spirit in this passage. We know Paul was speaking, but we don't know if the Spirit was working within Agrippa or not. He certainly wasn't changing Agrippa's heart, or Agrippa would have responded differently.
3. It seems the Agrippa was almost persuaded of the reasonableness of Christianity--a sort of mental assent, if you will--but he didn't realize the true value of it or he wouldn't have rejected it.
4. The failure was Agrippa's. It wasn't Paul's because Paul's presentation of the gospel was, in itself, very convincing, yet Agrippa rejected it. If the the Holy Spirit was working in this situation with the purpose of bringing Agrippa to salvation, then of course he failed, because he didn't accomplish his purpose. That's the very definition of failure--not achieving the desired end or result.
The means of salvation is rooted in the righteous character of God. It's not as if God had all kinds of equal alternatives for means and chose the one alternative that fallen human beings won't do. There was no other means that could have been chosen given that God is righteous. That fallen human beings can't produce faith except by way of a heart change doesn't really play into things at all.
Why is faith the only possible means? Because God can't dumb down the requirements of the law and still be righteous. Those requirements are rooted in his own righteous character. He can't require less than perfect works from us. And of course, fallen human beings aren't going to produce perfect works.
That's where Christ comes in. He did the perfect works, he met the requirements of the law, and his perfect works are counted as us meeting the requirements of the law. We recieve his law-keeping on our behalf through faith. Why is faith so perfectly suitable as the means through which we recieve Christ's work? Because faith is ceasing from doing our own works, and trusting in the work of Christ. Faith is the only things that perserves "Christ alone."
And that's the thing that fallen human beings don't like. Our pride makes us want to contribute something. We want to produce some of the grounds for our salvation. But God can't accept our own imperfect works as the grounds (or partial grounds) for salvation and still be righteous. He can only give us Christ's righteousness through faith--through our trust in Christ's work. That since the fall, we invariably don't trust God doesn't mean that God can save us through other means.
Calvinists believe that people are justified (saved) by Christ's work alone, which we recieve through faith. Faith is necessary for salvation. It is indeed "believe and be saved." Regeneration (or being born again) is the first thing in our experience of the salvation process, but regeneration in itself does not save us. We are saved on account of Christ's work, which is received by faith, a faith graciously produced in us by the work of the Holy Spirit.