The government will have to absorb those people whose jobs will be replaced by automation. The government does not have the same 'productivity' requirements as the private sector. The choice will be between some form of welfare or public sector jobs that may in fact be welfare. Realistically, the government is already doing this. The military industrial complex is a form of welfare. Besides the people in the military we provide meaningful labor to a large swath of people across all states. If we were ever to pause and spend less, there will be a huge depression the likes of which we have never seen.
Obamacare is another example. The government props up failed or unnecessary industries all the time. Imagine if the US went to a single payer system. Suddenly, hundreds of thousands of health insurance related jobs will vanish. I am quite certain that is one of the reasons why things are not changing in health care. The powers that be see what the impact of such a policy would have at the scale of a country like the US.