I haven’t a clue. Seriously.
In the interest of science I’m willing to give it a try. I’ll need some expense money
For a liberal definition of what constitutes a margarita, almost indefinitely. But at the very least until hurricane season.
Quite some time, I believe. You’ve got your macronutrients covered (protein, fat, carbs), and if you’re making actual margaritas with lime juice, Vitamin C is covered. Cholesterol from the shrimp, as well as enough B12 & iron to keep you from getting anemic. The spongecake supplies essentially nothing but calories, but you do need calories. If you can get the baker to make it with whole wheat flour, your bowels will thank you, though. Not a lot of fiber in this diet.
But it’s a lot more doable than many of the “how long could you survive on a diet of…” hypotheticals we see around here.
Well, according to this site, sponge cake, as expected for a cake, doesn’t have much in the way of nutrients (and a lot of cholesterol, though I suppose you could get it with egg whites, but then there are people who eat several whole eggs a day, at 70% of your RDA each, for years without getting heart disease).
Shrimp has even more cholesterol per calorie, at 55% of your RDA per 84 calorie serving, but more vitamins and minerals, including Vitamin C, but just 3%, although multiple servings could provide you with enough to prevent scurvy, but still less than optimal amounts (and far more cholesterol than is recommended, but again see my comment about eggs).
As for margaritas? I hope that isn’t all you plan to drink because that would quickly add up to a lot of alcohol, and no other nutrients to speak of, plus alcohol can inhibit the absorption of other nutrients.
At least until you come to the realization that it’s your own damn fault. In the mean time, you’ll be wasting away.
I’d ask Jimmy Buffett. He’s probably done it and written a song about it.
There’s no fat in that diet; Rabbit starvation, dying from a lack of dietary fat, happens eventually, even if enough calories to sustain life are consumed.
Does it help if the shrimp are eaten with the heads still on? I think there’s some fat in among the organs and such.
Not really; the links I posted lists sponge cake as having 2.7 grams of fat per serving and shrimp 1 gram (3.7 grams and 270 calories for both together, and you’ll eat multiple servings a day). Less than 10% of calories from fat, but more than “none”, and also some actual diet plans out there.
There is fat in sponge cake, surely (actually Michael63129’s link lists it at 13% fat, and all that cholesterol he is worrying about is a type of fat too), and there must also be some fat in shrimp: in their cell walls for a start.
That’s the key right there. A margarita can have almost anything added to it, including broccoli.
C’mon, guys—let’s get serious here. Purina Lab Monkey Chow and beer: can it be done indefinitely? I have little time or motivation for cooking anymore.
Sponge cake has milk, butter and eggs in it. Perhaps you’re thinking of angel food cake, which is fat free.
I’d make it through about the third 'rita, then pass out.
You’re right, I was totally thinking of angel food cake.
Whew! Close one. 
So how come angels don’t wind up with “rabbit starvation” then?
That’d help. Nice glob of orange fat in there as well as the (tiny) brain. Shrimp bisque is awesome if you make the stock for it with the heads as well as the shells.
Live?
Hell, this sounds like the perfect way to commit slow suicide.
Eat the chitinous parts of the shrimps’ tails. Decent fiber.