That's some advanced stuff you're trying to do there. I can think of a few different methods but they're all rather complex.
Graphically speaking, you might want to look into mesh distortions for your sprite. There are a few examples around the forum that might help you out. As for the physical act of squeezing your player, what sort of game mechanic are you talking about here? Top-down? Platform? The method in which you do this would be rather dependent on that.
Also, is your character an actual round blob, or is it just like a regular person, only squishy?
If it's an actual blob, you might want to check this out:
Obviously the code isn't all that important, but the theory behind it helped me make a physics blob using Construct. I'll post the example if you like, but it's rather a complex operation.