Trump, on Twitter, described the discussions as "moving along nicely", but decisions have yet to be made on such problematic issues as automobile tariffs and resolution of the US allegations of Chinese theft of intellectual property, forced technology transfers and computer hacking.
It remains unclear whether the US will cancel some or all of the tariffs the president imposed past year on more than $250 billion worth of Chinese imports.
Some of the most hard hurdles lie ahead as Chinese Vice Premiere Liu He arrives to continue talks with his counterparts Robert Lighthizer, the country's top trade envoy and Treasury Secretary Steven Mnuchin.
The limited time frame raises questions about how much a deal would reshape the longer-term economic relationship, rather than simply serve as a political win for Mr Trump that would last through his potential second term as the 2020 election campaign kicks off.
At first, pay attention to the trade negotiations between the USA and China.
Now, Vice Premier Liu He, a close confidante of President Xi Jinping, is leading a Chinese team to Washington.
The two countries had originally hoped to reach an agreement by March 1, but even as the negotiations have extended well beyond that date, Trump and his economic advisers say the discussions are progressing. We have to get a great deal, as the president says, that works for the United States.
A final sticking point appears to be when and how Washington will agree to lift the steep tariffs it has placed on more than $250 billion in Chinese imports.
One likely scenario to reduce mandated purchases is that USA negotiators push for Beijing's removal of a requirement that foreign companies partner with Chinese entities to do business in the country.
The United States and China "expect to make more headway" in trade talks this week, White House economic adviser Larry Kudlow said on Tuesday as the top US business lobbying group said differences over an enforcement mechanism and the removal of USA tariffs were still obstacles to a deal.
China, by contrast, wants the imposts dropped immediately and has signalled it won't agree to such punitive measures as they would erode its sovereignty.
The United States is seeking reforms to Chinese practices that it says result in the theft of US intellectual property and the forced transfer of technology from USA companies to Chinese firms. "Stand firm" Senate Minority Leader Chuck Schumer, D-N.Y., said Tuesday. In retaliation, China has targeted $110bn in American imports. He added that they have agreed to more things than what's left to agree on. The presidents want a deal, and they need to get through the end-game issues.