Right of Conscience also known as the Freedom of Conscience or Natural Right, is a judgement of right and wrong whereby human laws are invalidated if they infringe on the religious beliefs of an individual.
Healthcare Right of Conscience
An example of a Right of Conscience in healthcare would involve Christians healthcare workers refusing to provide services such as abortion, artificial insemination, contraception and end-of-life issues. Ethical medical care has been the foundation of medicine for over 2500 years, as defined by the Hippocratic Oath. 
Challenges to Healthcare Right of Conscience
Charges of discrimination hound those individuals that refuse to provide services against their beliefs. Liberals and their supporters (e.g. Planned Parenthood) are directly opposed to the Right of Conscience. 
Seven states sued the federal government over the new rule that expands protections for doctors and other health care workers who refuse to participate in abortions because of religious or moral objections. The states suing; California, Illinois, Massachusetts, New Jersey, Oregon and Rhode Island joined Connecticut in the lawsuit. In a separate lawsuit, Planned Parenthood of Federation of America Inc. and National Family Planning and Reproductive Health Association are suing as well.
Health and Human Services HHS Secretary Mike Leavitt has implimented the Right of Conscience rule as a final regulation before the Obama administration takes office. "Doctors and other healthcare providers should not be forced to choose between good professional standing and violating their conscience."
Founders Speak of Conscience
"No provision in our Constitution ought to be dearer to man than that which protects the rights of conscience against the enterprise of civil authority."
"Man has been subjected by his Creator to the moral law, of which his feelings, or conscience as it is sometimes called, are the evidence with which his Creator has furnished him... The moral duties which exist between individual and individual in a state of nature, accompany them into a state of society...their Maker not having released them from those duties on their forming themselves into a nation."
"…a man's land, merchandise, or money is called his property…He also has a property of peculiar value in his religious opinions and in the profession and practice dictated by them…Government is instituted to protect property of every sort…Conscience is the most sacred of all property."
"The freemen of America did not wait till usurped power had strengthened itself by exercise, and entangled the questions in precedents. They saw all the consequences of the principle, and they avoided the consequences by denying the principle. We revere this lesson too much, soon to forget it."
"The laws of nature are the laws of God, whose authority can be superseded by no power on earth. A legislature must not obstruct our obedience to Him, from whose punishment they cannot protect us. All human laws which contradict His laws we are in conscience bound to disobey."