Here's the wingnut dynamic. Republican lawmakers know exactly what budget reconciliation is. They know what the "nuclear option" is, too. And they're cynically tricking their mouth-breathing followers into believing those two things are the same.
They're not.
Budget reconciliation is an often used part of the Senate rules that calls for a majority vote to pass budget-related legislation. It's majority rule. No trickery or rule bending here. The filibuster doesn't apply at all. No filibusters. However, the opposition party can present hundreds of amendments within a set period of time. Some or most the amendments can be politically motivated -- designed to trap the majority into voting for or against provisions that could be used against them during a campaign. The Senate parliamentarian has considerable power over these proceedings.
The so-called nuclear option, on the other hand, isn't in the Senate rules. It's generally defined as being a way to break a filibuster with only 51 votes instead of the mandatory 60. The only way this can happen is if the Senate declares the filibuster to be unconstitutional. It was the Republicans who popularized this process throughout the Bush administration.
The Republican blending of the two options should probably be defined as the NOO-kyoo-ler Option. They know exactly what they're doing and they're clearly taking advantage of people who don't know any better. Like always. Actually, this pretty much defines the modern Republican Party -- tricking its own people with nonsense and hackery.