The cross and the resurrection of Christ are like load-bearing walls for the Christian faith.
The Sadducees didn't believe in many of the things Jesus preached. They had political power and were violent. They were mainly focused on this life and believers were warned to be aware/weary of these people as they pick and choose what to believe from God's Word.
The Sadducees were looking to mock Jesus's teachings when they questioned Him (that the idea of the resurrection is ridiculous); they weren't truly looking to learn. Their question may have stumped other religious leaders so when Jesus was able to respond, they were shocked.
Just like Jesus, we have a responsibility to correct those who have erroneous interpretations of God's Word. If there is no marriage in heaven, then their whole question has no bearing.
Jesus then refers to a passage in Exodus (the Sadducees only recognized the first five books as true). Pointing to the burning bush segment as God made a convenant with specific people, and in order to deliver on these promises those people must be alive. Therefore, they must be resurrected for the fulfillment of God's Word.
The other religious leaders could see Jesus' wisdom and how the people responded. And since they couldn't find an argument, they plotted to have Him killed.