1 Timothy 2:1-4 (NIV)
I urge, then, first of all, that requests, prayers, intercession and thanksgiving be made for everyone--for kings and all those in authority, that we may live peaceful and quiet lives in all godliness and holiness. This is good, and pleases God our Savior, who wants all men to be saved and to come to a knowledge of the truth.
The Bible exhorts us, as a matter of first priority, that we pray for those in authority. This starts with our president and continues down to the local level. We are to pray even for those with whom we disagree. The clear goal of such prayer is so that we can live in peace, able to concentrate our activity on spiritual matters. Perhaps it will not always be like this. There is a connection with this goal of peace and holy activity to God's pleasure. He desires all me to be saved and come to a knowledge of the truth. How else can they do this unless they hear the message of the gospel.
I've heard my Pastor talk about how he and his wife pray for the President and the other leaders of our national, state, and city governments. I'm convicted, I am praying right now.