The line, “He who blesses Israel will be blessed and he who curses Israel will be cursed” is not in the Bible at all. That phrase is a misinterpretation of one verse, Genesis 12:3. In Genesis 12:3, God said to Abraham, “I will bless them that bless you, and curse him that curses you, and in you shall all the families of the earth be blessed.” The direct “bless-curse” line concerned Abraham alone, not Israel.
While I am a Christian and I believe the US should support Israel, that “verse” is not in the Bible.
The context of the blessing, as repeated elsewhere in Genesis, refers to Abraham and his descendants. (Genesis 26:3-4, 27:29, 28:13-15). However, you're quite correct to note that there is no such verse referring to Israel as it did not exist at the time of the original blessing.