Were the Jews expecting the Messiah to suffer at all?

When Jesus spoke about his future suffering it did not seem to register properly. For example: >(Matthew 16:22) Peter took him aside and began to rebuke him. “Never, Lord!” he said. “This shall never happen to you!” This raises the question: Did the Jews push the suffering of the servant Messiah (Isaiah 53) to the background of their mind, or was there no expectation that Messiah would suffer at all?