"Federal criminal law prohibits "rebellion or insurrection against the authority of the United States or the laws thereof," including incitement or assistance to such rebellion or insurrection. It also prohibits conspiring to overthrow the U.S. government, levy war against it or oppose its authority by force. Based on the organization's declared mission, there's little doubt that the Oath Keepers would view any impeachment action by congress as "unconstitutional" and therefore not to be obeyed. Although the group's current tweets come close to calling for rebellion or insurrection should that happen, there's been no indication that the U.S. Department of Justice is investigating. Are the militias drawing up plans for possible civil war, for example? Are they training? Are they stockpiling weapons? These are things that law enforcement should be investigating, whether under federal law or state law.
Although it is widely believed that the Second Amendment protects the right to form private militias, it does no such thing. The Supreme Court made this clear in its 2008 decision in District of Columbia v. Heller, explicitly reaffirming its own 1886 holding that "the Second Amendment ... does not prevent the prohibition of private paramilitary organizations." Indeed, they are prohibited by state constitutional provisions or statutes in all 50 states."