The first U.S. president I diligently prayed for was George W Bush which makes me feel, er, ineffective at best and a counter-indicator at worse. (I was inspired, by the way, in this endeavor by reading how Fr. John McCloskey was doing the same.)
The Bush presidency seems a disaster, especially with regard to Iraq, which cost so many lives and casualties, destabilized the Middle East, decimated the Christian presence there and ultimately gave us Obama. Hard to have faith in prayer for a leader after that, even when the leader himself is a serious Christian. Of course the answer is that a president has free will, like all of us.
My prayer might be tiny, like trying to push a boulder with a pinkie, but I picture it as a tug of war where one extra hand can tip the balance. Or like voting, where a single vote is pitifully, almost infinitely weak, except when it isn't. I still should vote and I still should pray.