According to the dictionary, an Oath is:
"Any type of attestation by which an individual signifies that he or she is bound in conscience to perform a particular act truthfully and faithfully; a solemn declaration of truth or obligation.
An individual's appeal to God to witness the truth of what he or she is saying or a pledge to do something enforced by the individual's responsibility to answer to God.
Similarly an affirmation is a solemn and formal declaration that a statement is true; however, an affirmation includes no reference to God so it can be made by someone who does not believe in God or by an individual who has conscientious objections against swearing to God. Provisions in state statutes or constitutions ordinarily allow affirmations to be made as alternatives to oaths.
In order for an oath to be legally effective, it must be administered by a public official. The law creating each public office and describing the duties of the official ordinarily indicates who is authorized to administer the oath of office. A spoken oath is generally sufficient; however, a written and signed oath can be required by law."
And the Oath they must take is: "I do solemnly swear (or affirm) that I will support and defend the Constitution of the United States against all enemies, foreign and domestic; that I will bear true faith and allegiance to the same; that I take this obligation freely, without any mental reservation or purpose of evasion; and that I will well and faithfully discharge the duties of the office on which I am about to enter: So help me God." (This is the Congressional Oath of Office. Different positions require different wording, but the idea is the same.)
Everyone that swears an oath (or affirmation) swore to uphold the Constitution. They didn't swear to uphold the laws that are written, but to uphold the Constitution. That means in making the law, the enforcement of that law, and how that law is used in Court.
When someone breaks, or violates their Oath, there are strong and serious consequences for that.
A Congressperson can be removed from office, a lawyer dis-barred, and a Judge pulled from his/her bench and dis-barred as well as all of their cases being suspect.
The Code in each State has different punishments for violating the Oath of Office for State Government workers. But the US Code is universal enough to be shown here.
5 US 7731 Section 8(5) says: "Knowing membership with the specific intent of furthering the aims of, or adherence to and active participation in, any foreign or domestic organization, association, movement, group, or combination of persons (hereinafter referred to as organizations) which unlawfully advocates or practices the commission of acts of force or violence to prevent others from exercising their rights under the Constitution or laws of the United States or of any State, or which seeks to overthrow the Government of the United States or any State or subdivision thereof by unlawful means."
The punishment for Congress for waging war on the Constitution (and thus the US Government) is found in a different section.
18 U.S.C. § 1918 says: "Whoever violates the provision of section 7311 of title 5 that an individual may not accept or hold a position in the Government of the United States or the government of the District of Columbia." (The conditions of who this applies to can be read at the link given.)
And another consequence for violating 7731 is a Civil Suit under 1983 law.When an Unconstitutional law is passed by Congress, upheld in court by the Judges and the Lawyers, the consequences for those actions are fairly strong. Lawyers are dis-barred, Judges impeached, and Congress people are removed from office and never allowed to hold office again.
Charges of Oath of Office are a serious thing. And not to be brought about without some serious facts to back it up.
And lastly, please remember, I am not a Lawyer. This is not legal advice, but merely my understanding of things that I found in the Constitution. If you wish to use this information, please consult a Lawyer.