Government as an entity cannot have a relationship with God. However, individuals who are agents of government may have such a relationship. It is they for whom we pray.
The many individual representatives among us will include elected officials, appointed administrators, and employed persons in specific tasks. They will represent three branches of government: administrative, legislative, and judicial and will be engaged at city, county, state and federal levels.
So, we pray for a great number of people around us . . . individual agents of government . . . that each is responsible to God in the exercise of their respective tasks.
Let's focus the prayer more tightly. We ask our Heavenly Father to draw these men and women to intentionality, attentiveness, and responsiveness in their individual responsibility to God to the end that His will is performed at all times and in all matters.
Intentional - done on purpose; deliberate.
Attentive - paying close attention to something.
Responsive - readiness to act in performance of an obligation to do something as part of one's job or role.
Imagine the possibilities! Our prayer is aspirational and intercessory as we ask God to bring about a great turning to himself by an enormous number of people who are, collectively, government.
It seems to be a daunting undertaking until you consider God's promise to a government official a long time ago. Communicated to King Solomon and recorded in 2 Chronicles 7:14-15, "Then if my people who are called by my name will humble themselves and pray and seek my face and turn from their wicked ways, I will hear from heaven and will forgive their sins and restore their land. My eyes will be open and my ears attentive to every prayer made in this place."
We pray from position . . . humble, lingering in God's presence, seeking Him intently and personally, and repenting of sin . . . believing God will do exactly what He promised . . . hear, forgive, and restore. We do not define restoration. That is God's business. But, we can trust that it is good . . . very good!
Praying for evidence of good government . . . that it be responsive to God.
A worthy endeavor in the middle of His promise.
Pray and expect God!