The U.S. and China may not be able to lock down a firm "phase one" deal before the next tariff deadline in mid-December, according to a senior executive at the U.S. Chamber of Commerce.

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."