Lorie Smith claims legislation in Colorado could be used to force her to create websites promoting same-sex marriages if she also produces content celebrating the union of one man and one woman.
She said: "Since filing a lawsuit to protect my First Amendment rights on September 20, I have been bombarded with many messages about my case. Some have been supportive, but many more have been hate-filled and deeply unsettling."
The case, brought by Smith and her studio, 303 Creative, is being supported by Alliance Defending Freedom (ADF), a Christian legal organisation advocating for the right to freedom of faith.
ADF senior counsel, Jeremy Tedesco, said: "Artists shouldn't be threatened with punishment for disagreeing with the government's preferred views. The state must allow artists the freedom to make personal decisions about what art they can and can't create."
Smith's lawyers argue Colorado law falls foul of several aspects of the US Constitution, including clauses in the First Amendment concerning free speech and freedom of the press.
Smith went on to say: "To my clients who have received harassing messages because of the lawsuit,
I am very sorry that some people are so intolerant of my beliefs ...as to harass you.
"As you know, I try to treat everyone with respect and I wish they would do the same. Please contact me if you have concerns.
"To those who have filled my inbox with vile, hate-filled messages, if we disagree, we should be able to do so civilly. That is the mark of a healthy and free society."
Smith's lawyers believe she and her business could face fines of up to $500 for each violation and re-education training if they are found to have broken Colorado law.
Smith's lawsuit, referred to as a pre-enforcement challenge, is an example of an individual mounting a legal action against legislation before the government enforces it against them.