I consider myself libertarian, but welfare is the last thing I'd cut. It's true that the notion of welfare strengthening the overall economy is rooted in fallacy (ignoring unseen costs--read Hazlitt or Bastiat), but if we could do things like cut military spending drastically, let banks fail, get real currency, eliminate the income tax, the drug war, etc., it would have such a huge positive impact that very few would even need welfare once things got straightened out, and it would be a much easier pill for people to swallow politically--less destabilizing and divisive. Imo, it's stupid for libertarians to even talk about welfare. Just focus on getting rid of the things that have the biggest impact, and that almost everyone hates anyway, then go from there.

I'm not sure how cutting military spending (meaning laying off engineers designing weapon systems, welders putting together weapons systems, and cutting back on the number in the armed forces), letting banks fail (laying off people), ending the drug war (which means saving money by laying off policemen) will lead to reducing the expenditures on unemployment. Maybe long term it will lead to improvement but short term, cutting government spending equates to cutting jobs.

The money the government spends doesn't just get burnt into thin air. It gets paid out in a bunch of government contracts, those contracts buy products and services provided by private companies. Those private companies employ a lot of people and buy more products from other companies that employ a lot of people.

For better or worse, you need to recognize what happens when you cut government spending (a lot of people get fired, a lot of companies lose contracts) if you want to understand why people oppose cutting it.