Over the years I have known a number of men and women who were devout Christians and who also held public office–sometimes on a very high level. Yes, they felt the same pressures you mention–but in the midst of them they sought to do what was right, because they believed God had called them to their position.
The Bible actually gives us glimpses of people who had positions of responsibility but also sought to follow God. Job was a city leader who was known to be "blameless and upright, a man who fears God and shuns evil" (Job 1:8). During one of Paul's missionary journeys, a Roman proconsul (or governor) committed his life to Christ (see Acts 13:4-12). Erastus, the director of public works in the city of Corinth, was a Christian (see Romans 16:23).
Seek God's will as you make this decision. Our society needs more men and women in public office who are honest and capable, and perhaps it is God's will for you to be one of them. If people of integrity completely abandon politics, who will be left?
Whatever you do, make it your goal to live for Christ and to follow Him, no matter what the pressures are. The Bible's words apply to every Christian: "Be careful to do what is right in the eyes of everybody" (Romans 12:17).