A deal is would be seen as a step in de-escalating trade tensions between the world's two largest economies.
But some of that enthusiasm has dissipated since Chinese Vice Premier Liu He's Washington visit in October, said Myron Brilliant, executive vice president and head of international affairs at the U.S. Chamber of Commerce. Liu is also the chief trade negotiator for China.
"I explained to (Liu He), 'you're going to have to have some give-and-take here.' China has to bring more to the table in the final package," said Brilliant told CNBC's "Squawk Box" on Friday.
"This is the sixth time I've sat down with Liu He in two years. What I said to him is 'Don't overshoot.' China very much wants to see a rollback on the tariffs. By the way, so does the American business community," he said, adding that the levies have affected consumers, retailers, manufacturers and farmers alike.
"But we're not going to see an elimination of all the tariffs after phase one."
Trade tensions between the economic powerhouses have lasted for more than a year, with both countries applying tariffs on billions of dollars' worth of each other's products. Those moves have roiled global markets, plunged businesses into uncertainty and dented economic outlooks around the world.
Last month's negotiations resulted in both sides agreeing to what U.S. President Donald Trump was described as a "very substantial phase one deal" that would address U.S. concerns on intellectual property and financial services access and include sizeable purchase by China of American agricultural products.
China has said it would like to see the U.S. cancel additional tariffs and roll back duties as part of the agreement. But Trump cast doubts on the idea that Washington could agree to cut back tariffs as part of an initial agreement. He even threatened additional duties on China.
The next tariff deadline is Dec. 15. If the two sides cannot pen down a deal by then, additional U.S. levies on Chinese exports will go into effect.
When asked if he thought a deal could be inked by then, Brilliant said, "We're going to have just a few weeks now and I'm not sure we're going to get a deal done by Dec. 15. I hope so, I want to continue to emphasize there is an opportunity here between now and then, but we need more than Dec. 15 suspended."
On Sept. 1, the U.S. imposed 15% taxes on $112 billion of Chinese imports covering a wide range of consumer goods, including certain types of clothing and shoes, and some consumer electronics such as cameras and desktop computers.
"We need to see a rollback, I believe, on the Sept. 1 tariffs that were about a $112 billion," he said. "I don't think China should be having aspirations that go greater than that in terms of a rollback."
Overall, reaching a phase one deal would be an important starting point because it would put a trade truce between the U.S. and China, and prevent further escalation, Brilliant said. It would also "build a little confidence and certainty in the trading system."
Still, some of the more serious structural issues around Chinese subsidy practices and industrial policies are not going to be addressed in the phase one agreement.
— CNBC's Evelyn Cheng and Spencer Kimball contributed to this report.