BEIJING — After China’s president, Xi Jinping, ordered Beijing to cut its population, his protégé ordered the bulldozing of the homes of tens of thousands of migrants. After Mr. Xi told northern Chinese provinces to cut smog, cadres junked home heaters and stoves, leaving residents shivering.

These days when Mr. Xi speaks, officials from the top of the Communist Party to the lowest village committees snap to unflinching attention. The pressure on them may grow now that Mr. Xi has swept away a constitutional term limit on his presidency, strengthening his grip over the country.

But as these recent cases suggest, Mr. Xi’s daunting power may undercut effective policy or provoke public ire when lower officials scramble over each other to meet or exceed expectations, often leading to overreach and disarray.

“Whenever China has large-scale, top-down campaigns or initiatives, there are problems with overzealous officials and over-compliance,” said Elizabeth Economy, an expert on Chinese domestic and foreign policy at the Council on Foreign Relations in New York who has written a book on policy under Mr. Xi.