"Donald Trump convinced North Korea and China he was serious about bringing about change," said Sen. Lindsey Graham (R-SC).
"We're not there yet, but if this happens, President Trump deserves the Nobel Peace Prize," Graham said.
Last week, the President did not deny that he has been in personal contact with Kim Jong Un, as Mr. Trump shrugged off a question at a news conference with the German Chancellor.
"Have you spoken with Kim Jong Un himself?" a reporter asked.
"I don't want to comment on that," the President said.
Among foreign policy experts, some fear that Mr. Trump is getting played by the Pyongyang regime, that Kim Jong Un will say the right things about ending his nuclear ambitions, but not do so.
"Upon closer examination, there is very little of substance here," said Max Boot, a fellow at the Council on Foreign Relations, who has warily watched the Korean overtures.
"Two of North Korea’s biggest asks, over the years, have been a one-on-one meeting with US President, and a peace treaty, which could set the stage for US troops withdrawal," said Asia expert Patrick Chovanec. "Now it looks like both could be happening."
Certainly, a withdrawal of American troops in Korea - there since the 1950's - would be a major change.
"I don't have a crystal ball," said Defense Secretary Jim Mattis. "I can tell you we are optimistic right now that there's opportunity here that we have never enjoyed since 1950."
"It's taken a long time, many, many decades to get here," the President said. "Let's see what happens."