In this case, it’s the stretching of the region’s crust, and the movement of fluids through it, are causing these minor quakes. Far from being a danger, the USGS explains that they “actually represent an opportunity to learn more about Yellowstone.”
Sure, if Yellowstone were to catastrophically erupt today it would be genuinely devastating for much of the US and parts of the wider world.
Thankfully, it’s not going to. It’s not clear that Yellowstone’s magma chamber, which is undeniably colossal, is able to even trigger a paroxysmal eruption right now. A few months ago, Yellowstone Volcano Observatory’s Scientist-in-Charge, Dr Michael Poland, told IFLScience that “Right now, much of Yellowstone's magma body is partially solidified, and you need a lot of magma to feed a large eruption.”
Generally, you need 50 percent of it to be molten, but right now, that number’s around 15 percent. Even if a notable volcanic event did occur, it would most likely be a hydrothermal blast, or a lava flow, which are by far the most common volcanic activity types at the site over the past few million years.
You couldn’t even use a nuclear weapon to set Yellowstone’s supervolcano off. A surface detonation wouldn’t do anything at all, apart from, you know, kill everyone nearby.
So, in sum: No, shakes do not an eruption make.