This is speaking about blood curses, such as that placed on Jeconiah. Jeconiah betrayed God, so God cursed Jeconiah and all of his descendents. However, this blood curse is no longer in effect, as Haggai 2:23 shows a reversal of the curse. Most Jewish commentary suggests that the curse was lifted in Jeconiah's own lifetime, because of his own penitence, shown by the fact that he had children despite God's judgment, "Declare this man childless." Regardless, it is generally agreed upon in the Jewish commentary that this curse was lifted by the third generation, that is, of Jeconiah's grandson Zerubbabel, who reigned on the throne of David. The Jewish Ecyclopedia even says, interestingly, that Jeconiah would become the ancestor of the Messiah, and through Jesus' father Joseph, he was.
I think the important issue is that God will forgive all sin, except blasphemy against the Holy Spirit, which is a sin against oneself (Proverbs 8:36), as long as the person is penitent for those sins. The Hebrew Tanakh makes it quite evident that perfection is within our grasp, as anyone can obey the entirety of God's moral law:
"...if you will listen to the voice of YHWH, your God, to keep his commandments and his statutes which are written in this book of the law, and if you turn to YHWH, your God, with all your heart, and with all your soul.
For this commandment which I command you this day, it is not hidden from you, and neither is it far off. It is not in heaven, that you should say, 'Who shall go up for us to heaven, and bring it to us, that we may hear it, and do it?' Neither is it beyond the sea, that you should say, 'Who shall go over the sea for us, and bring it to us, that we may hear it, and do it?' But the word is very near to you, in your mouth, and in your heart, that you may do it.
See, I have set before you this day life and good, and death and evil..." (Deuteronomy 30:10-15)
Above, when God says, I present to you both life and death, good and evil, is talking about the nature of the Law as a blessing and the curse. Those who live by the Law will die to the Law, and their hearts will be transformed as righteous before God. But those who disobey the Law inherit its curse, and will die under it. The idea that we are incapable of perfectly obeying God is kind of silly. If ancient Jews could live by all 613 Mitzvot without any violation, Christians should have no problem obeying only the moral portion of the Law.
Many argue that there are none righteous, and that all need faith in Jesus to get to Heaven. This is not what the Bible teaches. In the Bible, there is no original sin. Instead, their is original virtue (God made man, and it was good). There is no unreachable perfection, for righteousness is not sinlessness, but the ability to overcome sin and serve God. Even Jesus said he did not come for the righteous, but for the sinner. That there arerighteous people is given by the dozens of verses that specifically apply to people and clans existing at the time the texts were written. That some people have attained perfection is given in that Moses, Noah, Zachariah and Elizabeth, Job, and others were declared righteous before God.
The message of the Bible is that God is love. Plain and simple. Betray God, and he will judge you rightly. Love God, and he will show you mercy. Compare this with the following verse:
"The fathers shall not be put to death for the children, neither shall the children be put to death for the fathers: every man shall be put to death for his own sin." (Deuteronomy 24:16)
This should make a bit more sense now, I hope. Be blessed.
