"I don't want to speak for the president, I don't want to lock him in, but I am confident what I just described with a few other things would be a deal acceptable to the White House and a lot of Democrats", Graham said.
President Donald Trump said yesterday he would not declare a national emergency "right now" to end a standoff over border security that has idled large swaths of the US government, all but guaranteeing that he will preside over the longest shutdown in USA history. "If we can't at the end of three weeks, all bets are off".
But if President Donald Trump is making his case that his signature anti-illegal immigration measure is urgently needed, he's not convincing Americans that a government shutdown is the way to get the wall built. Such a step would allow Trump to bypass Congress and tap various pots of unspent federal money, including for military construction and disaster relief and from asset seized by law enforcement, to pay for the wall.
After the shutdown slipped into the record books, with the impasse now entering its 23rd day, Mr Trump fired off a series of tweets saying he did have a strategy to break the deadlock. The president initially sounded as though such a move was imminent, but then pulled back.
Graham said he spoke with the president on Sunday morning, Fox News Sunday reported.
Turning to Twitter on January 13 Trump again pushed for the wall and pointed to Democrats to join in on the talks.
Although the president is now frustrated with the inaction of the Democrats, he does think this standstill could help Republicans in 2020. Such a move, should Trump ultimately go that route, would nearly certainly be challenged in the courts.
The paper reported law enforcement officials became concerned after Mr Trump fired Federal Bureau of Investigation director James Comey in May 2017 and said the agency had to consider whether the president's actions constituted a possible threat to national security. Senator Tim Kaine called the wall, which could cost an estimated $23 billion, a "vanity project" that Trump promised Mexico - not U.S. taxpayers - would pay for. Most came through our Southern Border.
Opponents say that a unilateral presidential move would be constitutional overreach and set a unsafe precedent in similar controversies.
Jennifer Lawless, a politics professor at the University of Virginia, said she believed Mr Trump and Republicans would lose the game of chicken as furloughed workers, travellers, tourists and others "experience the consequences of political dysfunction firsthand".
Trump has expressed interest in a broader immigration overhaul, but says he first wants the Supreme Court to address the class of immigrants known as "Dreamers". "I want to keep pressure on Democrats to actually come to the negotiating table in good faith and fund what they have supported in the past".
Instead, the president urged lawmakers to provide him the $5.7 billion he is seeking for border security.
Trump mocked them for "having fun" while he remains in snowy Washington.
Among Republicans, 58 per cent both support the wall and say Trump should continue to demand funding, compared with 22 per cent who say he should compromise to end the shutdown.
FILE - Vice President Mike Pence, center, looks on as House Minority Leader, now Speaker of the House, Rep. Nancy Pelosi, a California Democrat, and President Donald Trump argue during a meeting in the Oval Office of the White House, Dec. 11, 2018, in Washington.