WASHINGTON (AP) — One by one, the Republican senators floated their ideas. They were trying to find a way out of a seemingly impossible dilemma: how to support President Donald Trump's U.S.-Mexico border wall without approving the national emergency declaration he invoked to build it.

And one by one, during a private lunchtime meeting that ran hot at times, they found no easy answers.

As a deadline for voting looms, it's increasingly clear that Republican senators are deeply uncomfortable with Trump's use of executive power to build the wall and desperate to devise a way around the vote.

Senat...