Actually, the cost of bringing them all home would be VERY expensive. It cost money to get them there, and it costs money to bring them home. But, if you bring them home for long enough then you might save money in the long term. But since the military is paid salary and not hourly, I'm betting the cost savings would take years to reap.
And if you think you'll bring them home "during the shutdown" I can guarantee that you'll definitely be spending more money in the long run. But I don't think this was your intention based on your comment.
But ignoring these fact, if you chose to stop paying the military you'd have serious problems on your hands. Do you know what happens when the people holding the guns defending you do when you stop paying them? Well, let's just say "you don't want to find out". And the reality of it is that my military brothers and sisters would have serious problems because they can't expect to go get a temporary job while the wait out the shutdown nor do they have large sums of money to sit at home and still pay their bills.
I remember when Sept 11th happened and all sorts of government buildings were closed there was a lot of rumors that the military members might not get paid on time. Lucky for us many banks like Navy Federal Credit Union agreed they'd deposit our normal paycheck size into our accounts even if we didn't get paid. Many apartment complex came out and said that if we didn't get paid they wouldn't charge late fees if we didn't have our rent checks on time. Fortunately we did get paid on time and didn't have to worry about such things.
The last thing us military people needed to worry about when we were suddenly forced to go to sea unexpected(I was in the Navy) was to worry about if our family was home starving with no money and I was in the middle of the ocean unable to contact them to find out if they were even alive. Remember, the safest place for a ship is at sea. So guess where all the ships went when Sept 11th happened? That's right, to sea. Unfortunately many of us had families that were in panic over the Sept 11th attacks, and all that any of us knew was that we were going to sea for an indeterminate period of time, might or might not get paid on time, and no clue if we were going to war immediately or not.
So please think about the people defending your right to comment on this website before you start talking about not paying them. Because it stinks of shit when people like you talk out of your mouth with such rubbish. They didn't want the shutdown. And the very people that should be telling our Congress and President to go to hell when they do stupid things like this and voting them out are the same people that should be responsible for whatever consequences(good or bad) that come from not acting. So I don't feel too bad when the Grand Canyon, the WWII memorial, and the Statue of LIberty close. We wanted this. We asked for it by voting in these idiots. And by "We" that just means the majority. For the rest of us that didn't vote in these clowns, we should have worked harder to keep the clowns out of office.
So everyone enjoy the spoils from voting in these incompetent losers. You wanted it and you got it. And the worse you want it, the worse you'll get it. I know next election I'll be trying to get some fresh air in there.