Over what period of time did he indicate he wants to do this?
I used to think military spending was one of the few places spending shouldn't be cut, and I still believe it is the primary area that the federal government should be devoting significant resources too - it's one of the few appropriate functions of the federal government. However, having educated myself about the realities of our budget situation, I realize now that defense spending needs to be cut - significantly, though preferably over a period of time (5 or 10 years) rather than all at once.
For all that is wrong in principle, at least as far as my ideological sensibilities are concerned, with many of the smaller ticket spending programs, the big ticket items - the ones that matter most to the math, even if not the passions - are: Defense spending, Social Security, and Medicare. Our defense spending is too high, especially when we fairly include military pension and veteran's benefits costs (not that I'm advocating not living up to our obligations to veterans). We can't get to a reasonable level of fiscal responsibility going forward without doing something about defense spending or, in the alternative, significantly reducing Social Security and Medicare benefits. There's what you'd like to do and there's what you can afford to do, and at some point we're going to have to start considering the latter more so than the former.
If Gary Johnson is willing to be honest about our budget situation - in specific, about the need to cut defense spending - even though that honesty is probably unpopular with much of the Republican base, that makes me more likely to support him, not less.