Answer: Your concern over the Jews and their path to heaven is understandable given the New Testament record. The majority of the religious leadership in the first century A.D. rejected Jesus and his teachings. The Pharisees, for example, who were Jews, verbally attacked him to his face on several occasions (John 8:12 - 29, 48) and began to plot his death early in his ministry (Mark 3:6).
The scribes, who were also Jews, also sought to have him killed (Mark 11:27) and, along with the chief priests, challenged Christ's authority several times before his crucifixion (Matthew 21:23, Luke 20:1 - 2). It is easy to wonder how such people who reject the Lord as Messiah will make it to heaven.
Your question regarding the Jews, however, begs yet another interesting inquiry which is whether they believe heaven is their ultimate destination after they die. A 1906 Jewish Encyclopedia article states that they believe it is the location where God resides, but makes no mention of heaven being populated (either now or in the future) by those rewarded for their obedience. Instead, their understanding is that after the house of Israel is resurrected (Ezekiel 37) the destiny for Jews is with the Messiah in an earth-based kingdom.
For some sects of the Jews, any debate regarding how they will get to heaven after they perish is a mute issue. This is because they do not believe in a resurrection of the dead. The Sadducees, in Jesus' day, were a group of priests who operated Jerusalem's temple. It was widely known that they believed and taught that there was no resurrection (Mark 12:18 - 27, see also Acts 23:6 - 8), a point of contention between them and the Pharisees.
The apostle Peter, preaching to a large group of Jews on the Day of Pentecost, clearly taught that only through Jesus could a person receive salvation (see Acts 2:22 - 39). A short time later, the apostles were arrested for preaching the gospel.
The religious authorities of the Jews, who took the disciples into custody, wanted to know by what authority they were teaching people could be resurrected from the dead through Christ (which some feel leads to heaven, Acts 4:1 - 2). Peter boldly told them that there was only one way to be saved when he stated, " . . . for neither is there another name under heaven which has been given among men, by which we must be saved" (verse 12, HBFV).
Scripture does not teach that there are multiple ways to achieving the goal of eternal life. Every human who has or will ever exist, be they Jews or Gentiles, will eventually have to kneel before and acknowledge that Jesus is the Messiah (Philippians 2:9 - 11). The belief that heaven is our eternal reward is tackled in another article on this site. Suffice to say, any person who willfully and knowingly rejects the Lord as their personal Savior will not live into eternity.
The key to understanding the fate of the Jews in regard to heaven, and countless others not "saved" in this life, is that God's plan of salvation has three, not one, major parts. The first part, which ends when Jesus returns, is the calling of a relatively few number of people. These resurrected folks will help Christ rule the earth during the Millennium.
The second part of the Eternal's salvation plan is the saving of all those who live during Jesus' 1,000 year rule. The third part, occurring after the Millennium, is a resurrection of all those, including the Jews, whom God never gave a full chance to understand his truth. At that time He will open their minds to understand his words and give them an opportunity to be saved.
Our Father in heaven is more than willing to give eternal life to all those who repent and wholeheartedly accept his Son. In his wisdom, he has determined his redemption plan will occur in phases. It will be after they are brought back to life in the second resurrection that the Jews, along with countless others, will have their chance at salvation.