In answering this question, it's important to note the differences in how the state would likely respond now compared to how it responded to the historical Shays's Rebellion. Under the Articles of Confederation, there was not a standing national military. At this time, there also was not the kind of police infrastructure that exists today. Thus it took a while for the state and private actors to put together a militia.

Further, the kinds of military equipment that were available to Shays and his followers were on a similar level to those wielded by the militia that confronted him and his followers. The cannons wielded by the militia defending the armory in Springfield were more powerful than muskets, but this was not the kind of overwhelming inequality in power that is present between modern civilian firearms and military aircraft, for example.

However, this does not mean that such an uprising would be impossible, just that it would necessarily have to involve different tactics. Open conflict between civilian rebels and state militaries will go badly for insurgents, but many recent uprisings have been successful by foregoing military conflict and using protests/riots to destabilize state regimes. While a state military could brutally suppress such an uprising, it would be devastating to the legitimacy of most states.

Further, the use of decentralized groups of insurgents and of guerrilla tactics have both served insurgents well in rebellions in recent decades. We might imagine such an uprising against the extremely rich in the face of record levels of class inequality. We might also imagine an uprising against unjust, brutal policing. As faith in political institutions is quite low, we might even imagine a general uprising against the government. While the tactics of the late 1700s would be ineffective today, recent the recent rebellions of the Arab Spring and countless past rebellions make clear that when a sufficient number of people are angry with a government, they can find tactics that will be effective.