It’s really hard to ever prove anything in macroeconomics, but it is worth looking at the incredible surge in US economic output associated with World War II, a period during which normally politics was basically repealed and everyone just decided “F — it, we’re going to build as many tanks and bombs and planes as we can”:
A few things jump out here. One is that by borrowing tons of money to build as many tanks and bombs and planes as possible, the US government was in fact able to drastically ramp up total production. Another is that this wasn’t a magical process, but related to the fact that the war came at a time when there was massive resource-idling due to the fact that the Great Depression had led many years in which we undershot the longer-term trend. The third is that while we certainly could do this today — massive mobilization to invade and occupy Iran and Pakistan maybe — we neither will nor should. It’s just kind of a coincidence that the Depression led to a war that was both gigantic and just.
But the point is that if there were some gargantuan endeavor that both political parties agreed it was worth undertaking, then there’s not some law of nature preventing the government from massively reducing unemployment quite rapidly. You simply need commitment to mobilizing real resources. The difficulty is in developing any kind of political or intellectual consensus around what would be worth doing.