Were Early Christians Lobbyists?

While there are several individuals converts mentioned in the NT who held "state jobs" (soldiers, politicians, jobs, etc.), is there any evidence from the NT that the early Christians tried to spread Christianity by way of Christianizing their political and state institutions?

It seems many contemporary religious leaders (especially of the evangelical persuasion) act as though this is their whole focus in life, yet I personally don't find any examples of it being done or taught in the NT. My best guess at this point is because those first century people had a better understanding of what it meant to accept that Christ was King.

There was no need to hunt down some local ruler or governor in Ephesus or Colossae or even the Emperor himself and try to persuade them to outlaw (for instance) homosexuality. Why? Because Christ is the true King and Ruler of the world and He has already outlawed homosexuality whether Caesar outlaws it or not. And if Caesar refused to outlaw it, that wouldn't make Christ any less truly in charge of the whole world; and if Caesar did outlaw it, that wouldn't grant Christ's laws any more authority or legitimacy than they already had. Christ has absolute, totalitarian authority. He doesn't need Caesar to "help" Him be King. Christ's decrees are *the* decrees over the world regardless of what Caesar decrees. Simply put, Christ is Lord and Caesar is not.

Maybe i've misunderstood the project, but it appears to me that at least some mainstream evangelicals act as though Christ needs America's legal system to "help" Him be King.