Question

What does Eurylochus mean when he says, "I’d rather die at sea, with one deep gulp of death, / than die by inches on this desolate island here!"

Answer 1

is that Eurylochus was attempting to convince the rest of Odysseus' men to slaughter and eat the sacred cattle of Helios, the sun-god.

Answer 2

The answer is that Eurylochus was attempting to convince the rest of Odysseus' men to slaughter and eat the sacred cattle of Helios, the sun-god. Circe had warned Odysseus that his ships would be destroyed if he and his men ate Helios' cattle. Consequently, Odysseus made his men swear to leave the cattle alone.

Hope this helps!