Graham said he spoke with the president on Sunday morning, Fox News Sunday reported.
“I would urge him to open up the government for a short period of time, like three weeks, before he pulls the plug” on a legislative solution, Graham said.
Graham had earlier told reporters he would support Trump declaring an emergency in order to get the desired funds for dealing with what Trump claims is an immigration crisis on the southern US border, voicing frustration that Democrats in the past had voted in favor of funding some barriers on the border yet have so far resisted Trump’s demand.
"It really does perplex me how you expect this to end when you tell the president of the United States, 'you can't get… $1 for a wall when in the past Democrats have appropriated billions for the wall," Graham said, noting that Trump is “not going to give in” on the fight for border security yet.
"I don’t want to speak for the president… but I’m confident what I just described with a few other things would be a deal acceptable to the White House and a lot of Democrats, and I'm just so frustrated we can't get in a room and hammer it out," Graham said.
The US government entered its longest shutdown in the nation's history on December 21 after Democrats blocked a bill on the 2019 budget. Democrats have refused to give their support as long as funding for the construction of a wall on the southern border is included. Trump has insisted on funding for a wall that he says is aimed at stopping human and drug trafficking across the border, asserting that he will not sign a budget bill without funding for his promised wall.