After these things came Jesus and his disciples into the land of Judaea; and there he tarried with them, and baptized.
And they came unto John, and said unto him, Rabbi, he that was with thee beyond Jordan, to whom thou barest witness, behold, the same baptizeth, and all men come to him.
When therefore the Lord knew how the Pharisees had heard that Jesus made and baptized more disciples than John, (though Jesus himself baptized not, but his disciples,)
1 Corinthians 1:10-17
Now I beseech you, brethren, by the name of our Lord Jesus Christ, that ye all speak the same thing, and that there be no divisions among you; but that ye be perfectly joined together in the same mind and in the same judgment. For it hath been declared unto me of you, my brethren, by them which are of the house of Chloe, that there are contentions among you. Now this I say, that every one of you saith, I am of Paul; and I of Apollos; and I of Cephas; and I of Christ. Is Christ divided? was Paul crucified for you? or were ye baptized in the name of Paul? I thank God that I baptized none of you, but Crispus and Gaius; lest any should say that I had baptized in mine own name. And I baptized also the household of Stephanas: besides, I know not whether I baptized any other. For Christ sent me not to baptize, but to preach the gospel: not with wisdom of words, lest the cross of Christ should be made of none effect.
What I understand from this is that in first century Judea and perhaps beyond, baptism was understood to indicate that the person was a disciple of the baptizer. The disciples baptized "in the name of" another - namely at first Christ and later the Triune name, when it was revealed:
Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you alway, even unto the end of the world. Amen.
What the above would also seem to imply is that Jesus baptized the twelve (who then baptized others). But that would seem to imply that Jesus baptized Judas, who never had saving faith. Moreover, it seems readily apparent that Jesus knew Judas did not have saving faith.
Given that understanding of these texts, these texts seem to torpedo one of the arguments used against infant baptism, namely that baptism ought not to be administered to anyone who lacks faith.
One thing I've pointed out from time to time to my friends is that I don't see any specific, explicit Biblical limitation on Baptism. The Scriptures nowhere warn against baptizing folks who do not believe, for example. There may be reasons not to baptize everyone who claims that they want to be a disciple immediately (see Paul's point that he wasn't called to baptize).
Nevertheless, other times men have been baptized having known about Jesus for less than a day:
And the eunuch answered Philip, and said, I pray thee, of whom speaketh the prophet this? of himself, or of some other man? Then Philip opened his mouth, and began at the same scripture, and preached unto him Jesus. And as they went on their way, they came unto a certain water: and the eunuch said, See, here is water; what doth hinder me to be baptized? And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God. And he commanded the chariot to stand still: and they went down both into the water, both Philip and the eunuch; and he baptized him. And when they were come up out of the water, the Spirit of the Lord caught away Philip, that the eunuch saw him no more: and he went on his way rejoicing.
You should notice that in the above passage, Philip says that if the eunuch believes with all his heart, he can be baptized.
And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost. For they heard them speak with tongues, and magnify God. Then answered Peter, Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we? And he commanded them to be baptized in the name of the Lord. Then prayed they him to tarry certain days.
In the above passage, evidence of the work of the Spirit in the life of the people was sufficient grounds for their baptism.
And the keeper of the prison awaking out of his sleep, and seeing the prison doors open, he drew out his sword, and would have killed himself, supposing that the prisoners had been fled. But Paul cried with a loud voice, saying, Do thyself no harm: for we are all here. Then he called for a light, and sprang in, and came trembling, and fell down before Paul and Silas, and brought them out, and said, Sirs, what must I do to be saved? And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house. And they spake unto him the word of the Lord, and to all that were in his house. And he took them the same hour of the night, and washed their stripes; and was baptized, he and all his, straightway. And when he had brought them into his house, he set meat before them, and rejoiced, believing in God with all his house.
Here again is someone who appears to have been baptized within a day. The actual order expressed here is baptism, then belief, though one supposes that he believed first. But, in any event, no discussion of any limitations on baptism is provided here.
I don't mean for this post to be an expression of a lot of conclusions about the subject, but rather some thoughts on the issues surrounding baptism. The Bible does not expressly say that Judas was baptized, or that Jesus baptized the twelve himself.