“he sighed deeply in his spirit.” The word “spirit” is sometimes used to express an innermost part of a person or, more often in the case of God, when God is acting. In this case, Jesus’ “spirit” is simply a way of saying “sighed deeply within himself.” Some English versions try to make the English more understandable by translating the idiomatic use of “spirit” into more common English. Thus, the CJB says, “With a sigh that came straight from his heart.” The NIV simply says, “He sighed deeply,” and the NJB says “with a profound sigh.” The CEB tries to pick up some of the motion usually associated with the word “spirit” and says, “with an impatient sigh.”
The Pharisees had come to Jesus to test him and to ask him to do a spectacular sign. We can see how Jesus would have been frustrated and impatient with them, because he had done so many signs and miracles in the Galilee (he had just fed over 4,000 people with seven loaves of bread and a few small fish not too many miles away). Nevertheless, he was still hopeful he might reach some of them, along with the people he had not yet convinced of who he was (and he almost certainly would have been surrounded by people who were watching him closely). We can see why he would sigh deeply out of a mixture of frustration and hope, and then say that “no sign” would be given to them.
Mark’s record of this event gives us an important insight, because the Gospel of Matthew records the same event but records Jesus as saying that no sign will be given to them except the sign of the prophet Jonah (Matt. 16:4; Jesus also said that in a different context in Matt. 12:39). The fact that Matthew and Mark differ in exactly what Jesus said is profound, because what Jesus actually said was almost certainly recorded in Matthew, while what Jesus effectively said to the Pharisees, given the fact that no sign he ever did convinced them of who he was, was that “no sign” would be given to them. Thus, there was a sign for them, the sign of the prophet Jonah, but “no sign” was given to them that they accepted as a genuine sign, including his being raised from the dead.
“no sign will be given to this generation.” The Greek is more literally, “If a sign were to be given to this generation….” If Jesus was speaking Greek, this would be an anacoluthon, an unfinished sentence that is filled in in the minds of the speaker or hearer. However, there is evidence that it was a Semitic idiom that was basically a denial, so the translation “no sign will be given” is warranted.