The United States military is still the best fighting force in the world even with a government shutdown. Our troops fight willingly and won't abandon their posts as they defend our liberty in the name of God and country. The shutdown didn't compromise our security. Our severe debt problem will, in the future, do that if it isn't taken care of soon.
No, the government shutdown does not compromise American national security. National is security is one of the main things that remains funding for the most part during a government shutdown. Moreover, a government shutdown is more of a rhetorical tool used as a way to make the American people feel it at heart. When the government shut down results in shut down national parks, zoo, etc., the citizens actually see the effects but do not realize that behind the scenes many things are still functioning.