In the video below, Dr. James White discusses monergist salvation with a synergist.
I mostly agree with Dr. White's answers. However, as to the answer regarding the burning house, I'd have something else to say.
The analogy about the burning house is inaccurate, because the synergist does not assert that total passivity is the way that man is rescued from sin. Instead, the synergist asserts that man cooperates with God in order to be saved.
In other words, the situation is more like people hearing the voice of the fire marshall sounding through the smoky haze and some carefully follow his instructions and escape, and others ignore his instructions and perish.
Still, one might ask, do those who escape have any ground for boasting?
The intuitive answer is "no," but it is important to understand why that is.
Imagine there is no fire marshall at all. Some manage to escape the fire by strenuously exerting themselves to escape the blaze, and others die because they make bad attempts.
No, again, one might, do those who escape have any ground for boasting?
I still think the intuitive answer is "no," even though in this instance their salvation from the fire is entirely their own work. We wouldn't think people who bragged about how they escaped when others perished to be very nice people.
So, perhaps that's not quite what we mean by boasting. In other words, maybe what we mean by boasting is having any part in the credit for our salvation. In the last case, the escapees clearly can take credit. They used their wits or their muscles, or just their bravery to escape the fire.
But when we then reflect that back to the middle analogy where people cooperate with the fire marshall, we see that again those who are saved are those who are more obedient, more attentive, or have the good judgment to listen when others try to find their own way out. While they cannot take all the credit for their escape, it is a difference between them and the others that is the critical reason why they are saved and the others are not.
Even so in synergistic salvation. In synergistic salvation, man gets some of the credit, because man does some of the work. This detracts from the glory of God and contradicts Scripture. The former reason is enough to make the doctrine suspect, but the latter is the reason we reject synergism.
24Being justified freely by his grace through the redemption that is in Christ Jesus: 25Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God; 26To declare, I say, at this time his righteousness: that he might be just, and the justifier of him which believeth in Jesus. 27Where is boasting then? It is excluded. By what law? of works? Nay: but by the law of faith. 28Therefore we conclude that a man is justified by faith without the deeds of the law.
Praise be to the God who Justifies!