Promises are important. Promises from God are infinitely more important, and we must do all we can to correctly understand those things that God has promised to us. I hold Presbyterian and Reformed brethren in very high esteem, and gratefully accept them as brothers and sisters in Christ. However, on the issue of paedobaptism and who makes up the New Covenant, we just don't see eye to eye. Oftentimes in discussion paedobaptists will bring up Acts 2:38-39. Frequently they seem to throw this verse down as though it's supposed to be incontrovertible proof of their position, which has always confused me. Not only would I say it is not definitive evidence of paedobaptism, but it is not even relevant to the discussion! In fact, they wouldn't even want it to be relevant (but more on that later).

The Text

Typically, what is cited is Acts 2:38-39. However, if we want to capture a fuller grasp on the key concept of those two verses, I think it wise to go back to verse 33, and follow it through to 39:

Therefore, since He has been exalted to the right hand of God and has received from the Father the promisedHoly Spirit, He has poured out what you both see and hear. For it was not David who ascended into the heavens, but he himself says: The Lord declared to my Lord, ‘Sit at My right hand until I make Your enemies Your footstool.’ “Therefore let all the house of Israel know with certainty that God has made this Jesus, whom you crucified, both Lord and Messiah!” When they heard this, they came under deep conviction and said to Peter and the rest of the apostles: “Brothers, what must we do?” “Repent,” Peter said to them, “and be baptized, each of you, in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit. For the promise is for you and for your children, and for all who are far off, as many as the Lord our God will call.”

What is the Promise?

When we look at these verses together, we are equipped to answer the most important question of vv.38-39: What is the promise? Is this not the key question? If we are to understand the identity of the ones to whom the promise is given, we must understand what the promise actually is! This is where paedobaptist presumption seems to run high. The way this passage is used by our paedobaptist brethren, we can only assume they believe that the promise is New Covenant membership. "New Covenant membership is for you, and for your children…" Now I must say, if that is what the text said, there would be no discussion. It would be the power-verse many use it as. But if we look at the wider context, the identity of what (more accurately, Who) the promise is becomes clear.
Look at verse 33. "Therefore, since He has been exalted to the right hand of God and has received from the Father the promisedHoly Spirit, He has poured out what you both see and hear." I have used markups to show you the three points of emphasis. Looking at what has happened to Jesus, He has received. He has received the Holy Spirit. The Holy Spirit was promised. He has received the promised Holy Spirit. Remembering that verse divisions are a product of the 16th century and not inspired, let's take another look at our text:

“Repent,” Peter said to them, “and be baptized, each of you, in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit. For the promise is for you and for your children, and for all who are far off, as many as the Lord our God will call.”

These exact same key words are used just verses later after they are applied to Christ!

There is no chance that they do not refer to the same reality. As Christ as received, those who repent and are baptized in the name of Christ receive. As Christ received a promise, so those in Christ receive a promise. As Christ received the Holy Spirit as the promise, so also His people receive the Holy Spirit as the promise. The identity of the promise in Acts 2:38-39 is the Holy Spirit.

This is extremely important, because if the promise is the Holy Spirit, then the promise is not explicitly Covenant membership.

Undoubtedly it will be argued that while Covenant membership is not the explicit promise, it is implicit in the text, and thus this passage is still relevant to the ongoing baptism debate. But this is dangerous territory. To take this passage as implying Covenant membership is not only unsupported by the text, it is actually injurious to the paedobaptist argument! Because the giving of the Holy Spirit is inseparably tied to salvation (see Romans 8:11), to connect the promise of Acts 2 to Covenant Membership is to entwine salvation and Covenant membership, exactly what the paedobaptist denies! Paedobaptism stands or falls on the ability for someone (i.e. an infant) to exist as a Covenant member while not being recognized as regenerate. For the paedobaptist, to tie the Promised Holy Spirit to Covenant Membership is to lose the war in the hopes of winning the battle.

To whom is He promised?

The second question is concerning the identity of those whom Peter offers the promise. Here the paedobaptist, without fail, identifies this text as an allusion to Genesis 17:7,

I will keep My covenant between Me and you, and your future offspring throughout their generations, as an everlasting covenant to be your God and the God of your offspring after you.

However, there is a kinsman redeemer closer than this passage, and we must first turn to it. But before that, a story:

Peter sat, ashamed of himself after denying his Lord, not once, not twice, but three times! How foolish he had been. He boasted of going to his death for Jesus, and now he sits, hearing his heart beat, while the heartbeat of Christ was deathly still.

Days pass, and to his amazement Jesus is risen! He is risen, indeed! The risen Savior looks at Peter and asks him a simple question: "Do you love Me?" Of course Peter does. He answers in the affirmative. "Feed my lambs". Twice more does this conversation repeat. As Peter denied Christ three times, so did Christ three times restore him to fruitful ministry. Peter's sin did not cut him off from the love of God.
Perhaps Peter was not present for the trial of Christ, but he undoubtedly heard about it. We read it in Matthew 27:24-25:

When Pilate saw that he was getting nowhere, but that a riot was starting instead, he took some water, washed his hands in front of the crowd, and said, “I am innocent of this man’s blood. See to it yourselves!” All the people answered, “His blood be on us and on our children!”

Remember, this was during Passover, one of the three festivals required by all Jewish males to attend. There was certainly a large crowd. Less than three months later, these same Jews would travel again to Jerusalem for Shavuot, also known as Pentecost. It is therefore reasonable to conclude that a fair amount of those present at the trial of Jesus, those who placed upon themselves and their children the blood of the Son of God, were now hearing Peter preach, particularly as he refers to "Jesus, whom you crucified".

What were they to do? The blood of Christ was on them. The blood of Christ was on their children. Surely their sin has cut them off from the Messiah. How full of joy must Peter's heart have been! As he was restored after his part in the death of Christ, so now he had the opportunity to proclaim restoration to these as well! The blood is on you, you say! The promise is for you, you are not prohibited from salvation by your action. The blood is on your children, you say! The promise is for them, your action does not damn them. Those who were present for the trial but not present here today? The promise is for them, for those who are far off. It is for all whom the Lord calls. So repent, be baptized, and receive this gift. Not everyone who was present that day, whom Peter said "the promise is for you" received it. But 3,000 people accepted the message, were baptized, and received Him.