Good question! Some of the prophecies they point to most often are those that talk about the kingdom that the Messiah will establish, with peace on the earth and the destruction of Israel's enemies. Passages like Isa 9:6-7 speak of this;

"For a child will be born to us, a son will be given to us; And the government will rest on His shoulders; And His name will be called Wonderful Counselor, Mighty God, Eternal Father, Prince of Peace. There will be no end to the increase of His government or of peace, on the throne of David and over his kingdom, to establish it and to uphold it with justice and righteousness, from then on and forevermore.  The zeal of the LORD of hosts will accomplish this. "

Now we know that Jesus did bring peace, first of all peace with God, and He will return with the saints at the end of the tribulation period and establish a world wide kingdom of peace. But the Jews say that since Jesus didn't bring in a kingdom or peace, that He could not have been the Messiah. What they don't understand is that the prophecies speak of two different appearances as we know from the New Testament.

It's interesting that many of their arguments today are exactly the same objections the Jews had in Jesus' day. There's an interesting site at http://askarabbi.com/ where questions are answered by several Jewish Rabbis. If you search the questions for "Jesus", you'll get a pretty good insight into modern Jewish thinking on the subject.