I'd like to see the States be proactive; push the issue: declare a state of invasion and start calling up their National Guard to address the situation while demanding the federal government honor Article 4, Section 4 of the Constitution — this would bring everything to a head: either the States have the power to protect their citizens or they are wholly subservient to the federal government; either the federal government will honor the explicit and unambiguous words of the Constitution or they will not.
Would it cause a civil war?
I think only if the Federal Government tried to use military might against the States that would exercise their sovereignty.