Were Jesus' followers really willing to die for what they believed?

Yes—though it's worth being careful about a popular but overstated version of this argument.

You'll sometimes hear that "all twelve apostles died as martyrs," offered as proof they weren't lying. The reality is more modest: most traditions about individual apostles' deaths come from later, less certain sources. What's documented much earlier is that James, the brother of the apostle John, was executed by Herod, and Stephen, an early Christian leader, was stoned to death—both events described in the earliest layer of Christian history, and both figures refused to stop proclaiming the resurrection under threat.

People do sometimes die for beliefs they were taught by someone else. It's a different, much rarer thing to die for something you personally claimed to have seen, when simply admitting it was invented would have ended the danger.

This doesn't prove the resurrection happened. It's strong evidence the earliest believers were sincerely convinced—not running a scheme they secretly knew was false.