The exact phrase 'smaller government' is triggering because it's been so politicized into being a left vs right concept, but when left leaning individuals seek to decrease the strength of ICE, decrease the rights/capacity/scope of law enforcement, limiting executive powers especially as related to war, and other such things they are themselves also directly appealing for a smaller government, in at least some ways.
I think this hypothesis (that 'anybody' would trend towards seeking smaller government) is even testable with things like Asian Americans. Many/most have roots from more social type societies, and predictably trend towards voting liberal in America as a result of such, to say nothing of historical issues. But they are leaning more and more conservative over time, to the point that at current trends they will likely be a majority conservative bloc within a few decades.
It's simply that once one sees what 'big government' amounts to in the US and the current state of the US government, it quickly leads many people to start running in the opposite direction. And once you start running from such, the opposite (self responsibility/reliability/etc) inevitably grows in proportion simply because there is no other choice.
That's not arguing small government is supposed to be good or bad, it's just saying what the American mindset considers important when judging things - which is on traits which align with its mindset over its history, not on whether or not the application of policy seems evenly distributed to all.