Samuel West, in a sermon delivered to the Massachusetts legislature in 1776, the same year that we declared our independence by appealing to our God-given rights to life, liberty, and the pursuit of happiness:

The most perfect freedom consists in obeying the dictates of right reason, and submitting to natural law. When a man goes beyond or contrary to the law of nature and reason, he becomes the slave of base passions and vile lusts; he introduces confusion and disorder into society, and brings misery and destruction upon himself. This, therefore, cannot be called a state of freedom, but a state of the vilest slavery and the most dreadful bondage. The servants of sin and corruption are subjected to the worst kind of tyranny in the universe. Hence we conclude that where licentiousness begins, liberty ends.

When it comes to declaring that a same-sex union is a marriage, that is a prime example of appealing to the concept of liberty as permission for licentiousness.