Lindsey Graham of SC urged the White House and Democrats to consider supporting what he called a "breakthrough" compromise on immigration that would allow President Trump to secure his $5 billion demand for border security funds and also codify protections for Deferred Action for Childhood Arrivals (DACA) and Temporary Protected Status (TPS) holders.
White House counsellor Kellyanne Conway said overnight that Mr Trump is not reaching out to Democrats, rather he's waiting for Democrats to reach out to him. Trump gets a variety of information, Kelly said, but goes with his instincts anyway.
They were also notable given Trump's insistence for most of his term that the border would have a wall, not the "steel slat barrier" he has pivoted toward in the past few weeks.
Having canceled his plans to travel to his estate in Florida for the holidays because of the government shutdown that started on December 22, Trump tweeted, "I am in the White House waiting for the Democrats to come on over and make a deal".
The shutdown, affecting about one-quarter of the federal government including 800,000 or so workers, began when funding for several agencies expired.
Graham told reporters he presented Trump with the idea for a "potential breakthrough" on budget talks during their two-hour lunch at the White House on Sunday.
Mr Kelly will leave the White House on Wednesday after 17 months.
"To be honest, it's not a wall", Mr Kelly said, adding the mix of technological enhancements and "steel slat" barriers the president now wants along the border resulted from conversations with law enforcement professionals on the ground.
Britain voices 'grave' concerns over China's Huawei
She still faces extradition to the USA and up to 30 years behind bars if convicted of breaking Iranian sanctions. They are former Canadian diplomat Michael Kovrig (left) and businessman Michael Spavor (right).
"The President likes the $5.6 billion that was in the House package", Conway said. "But we left a solid concrete wall early on in the administration, when we asked people what they needed and where they needed it". "But always saying wall or no wall is being very disingenuous and turning a complete blind eye to what is a crisis at the border".
It should be pointed out too that Mr Kelly himself had said early in the Trump presidency that it would be a wall, and not a fence. Now Democratic leaders are adamant that they will not authorize money for the project, calling it wasteful and ineffective.
"They said, 'Well, we need a physical barrier in certain places, we need technology across the board, and we need more people, '" he said. Mr Trump claimed the deaths were "strictly the fault of the Democrats and their pathetic immigration policies that allow people to make the long trek thinking they can enter our country illegally".
"The president would ask things like, "'Why can't we do it this way?'" Kelly said.
The House and Senate gaveled in and out of session in under five minutes on Thursday. But a previous attempt to reach a compromise that addressed the status of Dreamers broke down past year as a result of escalating White House demands.
"The president is firm in his commitment to make sure we get money for border security, and there will never be a 60-vote deal in the Senate that doesn't include money for border security-slash-wall". "Now we have to do it the hard way, with a Shutdown".
In the interim, thousands of employees of federal agencies such as the Homeland Security, Justice, Commerce, Interior, Transportation, Agriculture and other departments were staying at home on furlough or soon to be working without pay.
Pelosi spokesman Drew Hammill added that Democrats are united against the wall and won't seriously consider any White House offer unless Trump backs it publicly because he "has changed his position so many times".