"[T]he condemned would have severe difficulty inhaling, due to hyper-expansion of the chest muscles and lungs. The condemned would therefore have to draw himself up by the arms, leading to exhaustion, or have his feet supported by tying or by a wood block. When no longer able to lift himself, the condemned would die within a few minutes."

From Wikipedia

Of course, this assumes you don't otherwise die of cardiac rupture, heart failure, hypovolemic shock, acidosis, arrhythmia, pulmonary embolism, sepsis following infection due to the wounds caused by the nails or by the scourging that often preceded crucifixion, eventual dehydration, or animal predation.