It would save some on some social programs, but not healthcare, since that isn't paid for by the government now. Also not nearly enough to make up for the additional costs.
It would be more taking the place of things like welfare, which only some people even get, food stamps, housing vouchers, etc. Again, all things only the poor get now. But even rich people would get the same basic income these poor people are getting. The poor would find that an amount they now get is less than what they used to get combined for welfare, housing, food and utility subsidies. That's if we only took what we're paying now, and spread it among people who aren't getting benefits now as well.
The money really has to come from somewhere it is not going to help people now, which the only thing I can see that being is weapons we won't use and corporations not paying taxes.
I don't think the military reduction solution would be as hard as you think, given that the military protested the amounts they got in the most recent budget as too high!