Several GOP senators on Tuesday appeared skeptical about taking the controversial step, though they stressed they didn't know what Trump was planning. The senators added that they would prefer to resolve the border stalemate through legislation.

"Whether that rises the the level of a national emergency. ...My understanding is that was used right after 9/11, I think, I think the president needs to tread lightly here and make sure that's warranted," she said. "That's a pretty big and bold statement to use the statute in that way."

She added that the "best scenario" would be for Trump and congressional lawmakers to get a deal "without declaring a national emergency."

"Obviously it's been suggested and talked about, batted around, but I would prefer that we, again, get this resolved in the old fashion way which is two sides sit down at the table and work out a negotiated agreement," Thune told reporters.

Republican senators are keeping their distance from talk of declaring a national emergency to get funding for a U.S.-Mexico border wall, even ashas floated the possibility.“There is a hard way and there is an easy way to do things, and I think that would definitely be a hard way," he said.