Was the New Deal an attempt to save capitalism from collapse, a change in anti-government beliefs, or a liberal response to a unique crisis?
I would argue that these things are not mutuallly exclusive. The New Deal was a combination of all of these things.
The New deal was clearly a response to what has so far been a unique crisis. The Great Depression was worse than anything before or since. The New Deal was a liberal response to that crisis.
However, this does not mean that the other things are not true. There was clearly a worry among Americans that capitalism could collapse. There were worries that Americans would feel that capitalism had failed them. The New Deal offered a way to prop up the system rather than to see it fall,
Finally, the New Deal required people to change their beliefs about government. The programs would not have been accepted by the populace if the populace had not changed its views on government.
Overall, then, I do not think these things are mutually exclusive. I think that the New Deal had aspects of all of these things.