Fasting isn't a weapon of government or a weapon against government.

In the Old Testament people fasted during a time of danger or after a disaster. It's mentioned the first time in Judges.

(Judges 20:26 NIV) Then the Israelites, all the people, went up to Bethel, and there they sat weeping before the LORD. They fasted that day until evening and presented burnt offerings and fellowship offerings to the LORD.

Fasting is only mentioned twice after the resurrection of Christ. When and why you should fast isn't clear.

(Acts 13:2 NIV) While they were worshiping the Lord and fasting, the Holy Spirit said, "Set apart for me Barnabas and Saul for the work to which I have called them."

(Acts 14:23 NIV) Paul and Barnabas appointed elders for them in each church and, with prayer and fasting, committed them to the Lord, in whom they had put their trust.