There is no such right — in fact, there is obligation:
US Constitution, Art 4, Sec 4
The United States shall guarantee to every State in this Union a Republican Form of Government, and shall protect each of them against Invasion; and on Application of the Legislature, or of the Executive (when the Legislature cannot be convened), against domestic Violence.
Because the Obama Administration, knowing it has an obligation to secure the border, but which chooses not to do so, would be willing to MASSACRE AMERICAN CITIZENS who DO want it secured!
Or - We have an important obligation and we refuse to fulfill it. But if YOU, CITIZEN, try to do our job, we will KILL YOU!