Even though Lazarus was dead for 4 days, Jesus defied expectations and resurrected Lazarus from the dead. Martha and the Jewish mourners saw the resurrection with their own eyes.
From the resurrection, some of the Jewish mourners believed in Jesus because of what He can do (11:45). Jesus also talked about how the disciples can believe in Him even more. And for people like Martha who believed in Jesus but doubted Jesus can work with Lazarus, those people's faith were strengthened because they saw that Jesus is more capable than they originally thought of.
However, some people still did not believe in Jesus -- even after witnessing the resurrection. They demonstrate that miracles and sights do not guarantee belief in Jesus. Eventually, they met with the Pharisees. The Pharisees asked about what to do because they feel that if people believe in Jesus, they would lose their place to the Romans. From the statement, part of the motives to opposing Jesus is maintaining power and standing in the world.