The word "search" is ereuano in Greek, and means "to search, examine into." It can imply "to search by uncovering; to search minutely; to explore; to strip, to make bare; to search by feeling, by touch."
Homer, in The Iliad, used this word to indicate a lioness and her dedication to her cubs. They were lost, and she was on a huge plain searching very carefully everywhere. In The Odyssey, he used the same word to picture a dog tracking its prey - having its nose on the ground and never losing the scent.
Metaphorically, it can be used to describe one digging deep for treasure and precious metal, breaking every single clod that nothing would be missed. It means to shake and to sift until every meaning of every sentence, word, syllable, and even every letter may be known and understood.
Jesus is saying that these people search out every tiny, minute thing in striving for eternal life. But they were not willing to come to Him, humble themselves, and change so that they would have real, eternal life!
Can this happen to us today? Sure, it can! We see things that we are loathe to change in our lives, or we procrastinate. This is what Jesus is illustrating. Luke 18:9-14 gives us an example of a man who thought that he was doing wonderfully well. He probably knew more than the tax collector ever would. But the tax collector had the humility to humble himself before God and to repent.