What first amendment test requires the state to prove there is a high likelihood that the speech in question would lead to a danger that congress has the right to prevent?

The answer is "Clear and present danger test".

Clear and present danger was a precept received by the Supreme Court of the United States to decide under what conditions points of confinement can be put on First Amendment opportunities of discourse, press, or get together. Despite the fact that the U.S. Constitution's First Amendment ensures the right to speak freely, any discourse that represents an "obvious threat" to people in general or government loses this security. The great illustration is that yelling "Fire!" in a swarmed theater isn't ensured discourse.