One blockade that the SCOTUS loves to throw in the way of any case they don't want to face is the blockade of the plaintiff not having "standing". In other words, unless the senators and congressmen can show that they were directly and materially harmed by the war, the SCOTUS will more than likely throw the case out for lack of standing. I doubt being a congressman by itself establishes standing in the SCOTUS's eyes. I think that's usually a bullshit excuse on their part. Every American citizen should be considered to have standing for constitutional cases, because when the government violates the constitution we are all materially harmed. Unfortunately the SCOTUS doesn't see it that way.