The world wonders what — if anything — can restrain Trump on Greenland

As U.S. President Donald Trump's insistence on owning Greenland becomes even more vehement, there's a growing sense of urgency around the globe to figure out what — if anything — could change his mind.

So far, nothing appears to be dissuading Trump: not attempts by European politicians to flatter him, not diplomats' proposals for enhancing Arctic security, not polling that suggests Americans broadly oppose taking over Greenland, and not fresh stock market jitters.

During Trump's rambling, epic-length news conference Tuesday — where he spent an hour and 20 uninterrupted minutes touting his administration's accomplishments since his inauguration last year — three words jumped out regarding the standoff that threatens to rip apart the NATO alliance.

"How far are you willing to go to acquire Greenland?" a reporter asked. 

"You'll find out," Trump responded.  

While Trump has a track record of backing down on some of his most ill-tempered threats, those who want him to cease and desist on Greenland are struggling to uncover what would prompt him to give up this time. 

"I do not understand what you are doing on Greenland," French President Emmanuel Macron wrote in a private text to Trump, which the U.S. leader then posted on social media. 

Macron is far from alone in not understanding.

Until now, NATO allies have tried to satisfy Trump's thirst for control by offering to beef up their collective military protection of Greenland and reminding him of the 1951 treaty with Denmark that gives the U.S. basically unfettered access to build bases and station troops on the Arctic island. 

Trump rejected that alternative, insisting that anything less than U.S. ownership of Greenland is unacceptable, then threatened tariffs on Denmark and seven other European NATO countries for refusing to comply with his demands. 

The search for ways to give Trump a "win" on Greenland — something short of territorial ownership that he could still brandish as a deal-making accomplishment — is coming up empty. 

So if NATO, an alliance to which the U.S. belongs, can't persuade Trump to ease off the throttle, can the political party to which he belongs do any better? 

A few Republicans in Congress are starting to show some willingness to call Trump out on this issue. 

Some evidence of that was apparent on Sunday, when Americans tuning into the major network political programs saw GOP lawmakers criticizing the president's Greenland fixation.