One where moral issues are not put to the vote.
You suggest that anything decided upon by the majority of American voters that contradicts your morality makes the Government of the USA illegitimate?
What system do you think would be preferable? Where a ruling religious council can chose which candidates are morally unfit to run for office and be able to strike down laws that they see as immoral? That is the system in Iran, and the people don't seem to be big fans of it.