ISTANBUL — It was just before midnight a week ago Monday when three friends saw the bulldozer approaching the edge of the park.

“We got in front of it and called others, and from three people it’s come to this,” said Birkan Isin, a 40-year-old lawyer, as he gestured out the picture window of a cafe in a luxury hotel toward the thousands of people occupying Taksim Square.

Turkey’s leadership is facing its gravest political crisis in years, and it began with a few friends determined to save a park in Taksim who unexpectedly inflamed public frustration with a powerful prime minister, Recep Tayyip Erdogan.

But the protesters, in many ways even before the convulsion that has gripped the country, represented one side of a fault line that runs through Turkish society and politics. While the prime minister and his supporters are religious conservatives, the leaders of this movement are secular, leftist, liberal and, in Mr. Isin’s case, even a bit New Age.