The limiting factor in an all beer diet would not be cirrhosis of the liver which takes years to develop.
Rather there is a phenomenon known as beer potomania. It results from intaking excess liquids without enough salts. The kidney has a maximum diluting capacity(approx 50 mOsm/L), meaning that to excrete the fluids in 2 litres of beer you would also lose 100 mOsm of salts. Beer doesn't provide enough of these salts to actually excrete the volume you ingest. This would result in fluid retention with concommitant sodium and potassium depletion. Loss of those minerals would kill you first(not sure which one would drop to the critical value first).
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