The phrase that best describes the "cause" that Paine refers to is freedom from an oppressive government.
Explanation:
Thomas Paine claim for justice and equality for all people in America, he said that everybody had the right to live life in freedom and not under the rules of a government that will use them for their benefit, he wrote his statements in the pamphlet called "Common Sense" which is believed to be an inspiration for the revolution movement and latter the creation of the American Constitution.