Adding to the difficulty of reaching a deal has been the fractious nature of the Trump administration, with the three main government departments involved in the negotiations each pursuing a somewhat different agenda. Those different agendas to some extent reflect each agency’s institutional biases and responsibilities, but make it harder to predict what a final deal will look like.

Robert E. Lighthizer, the United States trade representative and a hawk on trade issues, has led the push to impose tariffs on imports from China and has pursued an ambitious agenda that would require China to carry out verifiable and enforceable changes to the basic structure of its economy. Mr. Trump said last month that Mr. Lighthizer would be the lead trade negotiator with China.

The Commerce Department, which oversees American export promotion activities overseas, and Commerce Secretary Wilbur Ross have been pushing since the early days of the administration for a deal that would require China to buy more food, natural gas and other products from the United States. Beijing officials have been happy to go along, as their country is short on arable land and gas, and long-term purchase agreements fit easily into the Chinese government’s economic planning model.

The Treasury Department, under Secretary Steven Mnuchin, has been pushing for a quick deal that would stop further increases in American tariffs. But Treasury would preserve indefinitely the 25 percent tariffs that Mr. Trump imposed in July and August on $50 billion a year in Chinese-made goods, or roughly a tenth of American imports, and the 10 percent tariffs that he imposed in September on an additional $200 billion in Chinese goods.

That first set of tariffs covers several categories in which China does not export much now but plans to do so in the next several years. The most important products covered by the 25 percent tariffs are gasoline-powered and electric cars. At least six Chinese automakers have announced plans to start exporting cars to the United States in 2020, said Michael Dunne, the chief executive of ZoZo Go, an automotive consulting firm specializing in China.

“Import duties will slow — but not stop — Chinese automakers’ plans to enter the U.S.,” he said. “With a slowing home market, pressure to export has never been greater.”

Democrats and Republicans alike have been wary of allowing an influx of Chinese cars in an election year, particularly when manufacturing states like Indiana, Michigan, Ohio and Wisconsin have been among the main electoral battlegrounds in recent decades.