Perhaps.
Considering we can't cut a dollar over ten years I think it would be best to think about what is at least remotely realistic.
I consider today's police force to be the standing army. Dissolve them. Sheriffs, perhaps. Locally. And even then restrained.
The army? People should be trained. If ever there was a time, which wouldn't be anytime soon, to be clear, that we needed an army mobilized and trained to fight another well trained and funded army, we should be ready. You asked somewhat of hard question to answer in such simple terms. Our diplomacy would have to change. Dollar hegemony ended. The people willing to work. Am I to assume these things happen? Seems to be wishful thinking. Besides all that the entire mind frame of the people would have to change. Indeed they would have to accept their safety as their responsibility. I believe in national defense but nowhere near what we have today. (which is so bloated and overbearing as it hurts national defense) We can have a well maintained and trained army for much cheaper than we do now. Cutting the DoD budget by upwards of 80% would limit how adventurous they really could be. Again though it doesn't matter unless the people change. Until they hold their Representatives and Senators accountable. Us harassing and bullying the world would have to be a thing of the past and that doesn't seem realistic anytime soon.
My answer would be, eventually, probably. As it stands, no. Though I would put them back to a 1990 or so level. CIA, NSA, and most of the other 15 or so intelligence agencies dissolved. The FBI dissolved. The DEA and TSA and BATF dissolved. A lot of people would be being prosecuted for their crimes as well. From the fraud charge dodging MIC to the politicians who violated their Oath of Office.
Time to wake up from the day dream. We will be bombing Syria and soon enough be in Iran. Conscientious objector, I suppose I'll have to be. I don't see a volunteer army lasting much longer.