They had two choices: leaving their ship, their supplies, their hopes and trekking ashore -- or staying put, with winter approaching, on a ship that could be crushed or released at any moment.
Stefansson argued that there was no point abandoning the ship unless they were forced.
But he soon made a more controversial decision. Taking some of the expedition's best dogs and five men, including McConnell, he set out for shore to hunt for meat.
The ship soon drifted away, and water opened up near shore, cutting off Stefansson's group from the Karluk.
In Stefansson's view, there was nothing more he could do for the Karluk, so he struck out along the shore, with his small party, to meet up with the rest of his expedition and his other two ships.
But he assured the world, in a dispatch to The New York Times, that on board the ship, "the men are in no grave danger, as the vessel is provisioned for five years, and equipped with suitable gear for making land if abandoning the ship become necessary."
Karluk or no Karluk, he said, his work would continue, and within a few months, he was off exploring the coast like he planned.
Stefansson's trip across the treacherous ice was not without its dangers. One morning, McConnell wrote, "we found ourselves afloat on a piece of ice about 20 feet wide." But it was the men he left behind who would soon be facing the deadliest conditions.
Remaining on board the Karluk were 14 crewmen, six scientists, five Eskimos and 27 dogs. They were mostly in their 20s, and aside from the Eskimos, few had any experience in being out on the ice.
They had with them enough provisions to last several years, much of which they unloaded onto the ice to be ready for anything. At a moment's notice, they had to be prepared to either abandon the ship immediately, if it was splintered by the ice, or to scramble aboard the ship instantly if the ice broke.
Gale force winds sometimes reached 60 mph, and temperatures fell below zero Fahrenheit for days.
The men knew they were drifting farther and farther from land, and the days were getting shorter and shorter.
It was clear that if the ice did not release them soon, they would become trapped throughout the winter and carried even farther away.
In spite of their plight, the men saw some memorable moments: enjoying the beauty of the Northern Lights; building a ski jump; hunting seals and polar bears; holding a chess tournament; and feasting at Christmas on canned delicacies such as ox tongue.
They even held a football game on New Year's Day -- although they stopped using the whistle because it froze to the lips and took the skin off.
But on many a night, "it was black as pitch, with a stinging snowdrift swirling through the air, driven by a screaming 50-mile wind," meteorologist William McKinlay wrote. There were often loud cracks and tremors, and the constant knowledge that "our lives were in imminent danger, and any day, any hour might be our last."
On January 10, 1914, after five months of being stuck, the ice finally crushed the Karluk.
The morning after it went under, according to crewman Ernest Chafe, "the place where she had sunk was completely frozen over, and every trace of the ship obliterated."
Now forced to sleep on the ice pack in igloos and lean-tos, the men had to avoid using sleeping bags. If the ice cracked, they would need their arms free to swim. One night, the shifting ice opened a gaping 2- to 3-foot-wide crack down the middle of one of the igloos.
"In a few seconds," McKinlay wrote, "there was a lane of water just where [two people] had been sleeping."
They couldn't stay put forever: the ice would break up beneath their feet come springtime, and they were drifting away on ocean currents, hundreds of miles to the northwest, north of Siberia.
They knew waiting for rescue would be a mistake, because no one knew their location and no ship could penetrate the ice. An attempt to make it to shore by sled team would be perilous, given the gale force winds, the bitter cold and the round-the-clock darkness.
The closest reachable land was almost a hundred miles south: Wrangel Island and the tiny neighboring Herald Island. After a few weeks, an advance party set out to blaze a trail to the islands. Their agonizingly slow trek was cursed with every impediment: blizzards, frostbite, soaked clothing, choppy ice, dogfights and openings of water that were hazardous to cross.