Too much protein=fat storage?

A nurse today told be that eating too much protein leads to fat storage! Is that possible, even on a caloric deficit?

Protein has a higher TEF (thermic effect of food - http://en.wikipedia.org/wiki/Thermic_effect_of_food) than carbs or fat, so in that sense is less likely to lead to fat storage when overeaten. That said, anything which represents a legitimate surplus in calories will "lead" to fat storage, even if the thing being stored as fat isn't that macronutrient. Meaning that you can make yourself fat by overeating anything, carbs, fat, or protein.

For example, overeating carbohydrate pretty clearly leads to fat gain, right? But it isn't because you're converting that carbohydrate to fat (under most circumstances), it's because you're impairing fat oxidation (fat you "burn" for fuel) with the overconsumption of carbohydrate, leading to dietary fat winding up as stored fat. Similar deal for protein - it's not that protein is being converted to fat per se, it's that you wind up indirectly impairing fat oxidation by overconsuming protein, leading to fat storage.

To address your hypothetical about protein consumption in a caloric deficit, fat storage is not possible from "overconsumption" of anything on a caloric deficit. Because, by definition, a caloric deficit literally means eating fewer calories than you're taking in. If you ate nothing but 400 grams of protein (a ridiculous amount, this is an intentionally absurd and unrealistic example) a day but needed 2000 calories to maintain weight, despite eating a ridiculous amount of protein, you'd lose weight, by definition, because you'd only be taking in ~1600 calories. Make sense?