I suspect you've learned, too, that prayer is the activity of the Holy Spirit. While we've prayed for the President, our nation, its leders, our society, our troops, and for God to be pleased to use our nation as one instrument of His work in the world, and we've seen Him answer prayers, the real blessing has been to be in His presence and to hear Him speak. It wasn't until we started this ministry of prayer that we came to understand that prayer is waiting upon Him to reveal His thoughts and His heart, so that we might speak what we saw and heard back to Him. It's been an amazing thing to be discipled by the Holy Spirit Himself in this.
You are so right. Unless you have experienced it, as we have, you can't fully understand it. We have been truly blessed!