The historical Jesus seems not to have contended in rabbinic battles with scribes, Pharisees, and Sadducees. In the gospels, he's always contending with them and getting the better of them, but these stories are a case of first-century Christians answering their critics by putting their own words into Jesus' mouth. Nor did Jesus have much to say about the afterlife. He certainly didn't believe that his followers would become angels in heaven after they died. With that context, here is Mark's version of a "controversy story"
Then the Sadducees, who say there is no resurrection, came to him with a question. "Teacher," they said, "Moses wrote for us that if a man's brother dies and leaves a wife but no children, the man must marry the widow and have children for his brother. Now there were seven brothers. The first one married and died without leaving any children. The second one married the widow, but he also died, leaving no child. It was the same with the third. In fact, none of the seven left any children. Last of all, the woman died too. At the resurrection whose wife will she be, since the seven were married to her?" Jesus replied, "Are you not in error because you do not know the Scriptures or the power of God? When the dead rise, they will neither marry nor be given in marriage; they will be like the angels in heaven. Now about the dead rising--have you not read in the book of Moses, in the account of the bush, how God said to him, 'I am the God of Abraham, the God of Isaac, and the God of Jacob'? He is not the God of the dead, but of the living. You are badly mistaken!"'
Mark 12:18-27, NIV
There's a common idea in everyday Christianity that people become angels when they die. You don't see it in biblical Christianity, just in popular imagery. You see it in Looney Tunes, when a character dies and floats like a ghost up to toward the sky with a halo, robe, and harp. You see it in Family Circus, too, when dead Grandpa, now with wings, leaves Heaven to zoom down to earth and intervene in the kids' lives. Apparently, the above scene from Mark's gospel contributed to this myth.
In this confrontation, the conservative Sadducees are trying to show that the resurrection doesn't make any sense. The idea of the resurrection comes from a literal reading of Ezekiel 37: 1-14. In this prophecy, Ezekiel brings dry bones back to life, symbolizing the rebirth of the nation of Israel. By Jesus' time, however, the Zoroastrian idea of Judgment Day had influenced Jewish thought, and the prophecy was taken by many to promise the actual resurrection of individual people. The Sadducees recognized this reading as extra-canonical.
Jesus dodges the philosophical trap by likening resurrected Jews to angels. It's a witty enough rejoinder that the Jesus Seminar ranks it as a gray "maybe." Geza Vermes gives it a solid No. Authentic or not, the teaching that the resurrected will be like angels in heaven lends support to a recurrent unorthodox belief that the resurrected will actually be angels in heaven. It's as if the phrase "are like the angels in heaven" gets read as "are angels in heaven.
The idea that people become angels after they die got a lot of play but never made it into orthodox teaching. Vermes cites the Book of Enoch as the earliest Jewish reference (3rd to 4th century BC). Among ancient Christians, Origen taught that humans souls, after death, would ascend or descend to lives as angels or demons, but his work was later judged heretical. The concept later appeared in Sufi teaching. It seems that the idea is so attractive that it has at last won out by popular demand."
Contributing to this misunderstanding is Plato's myth of Er, in which the good people go up into the sky for their heavenly reward immediately after they die. This myth contributed to the common Christian idea that one's heavenly reward (or infernal punishment) comes right after death instead of at the end of the world.
"Heaven" is the sky
Bear in mind that the term "heaven" in these verses should best be translated as "the sky." The "heaven" where angels were purported to live was a physical location up there above the clouds, not some spiritual dimension.
Husbands and wives
Also note that the Sadducees concocted a thought experiment about a resurrected woman with multiple husbands, not a man with multiple wives. Why? Because multiple husbands violated scripture while multiple wives did not. Monogamy is a pagan system that Christianity adopted as its own, but without scriptural basis.