Senator Lindsey Graham, R-S.C., said he hoped to end the shutdown by offering Democrats incentives to get them to vote for wall funding.
"We pushed the pause button", McConnell said the day the government was scheduled to partially close, "until the President, from whom we will need a signature, and Senate Democrats, from whom we will need votes, reach an agreement".
"They said, 'Well, we need a physical barrier in certain places, we need technology across the board, and we need more people, '" he said.
After canceling a vacation to his private Florida club, Mr Trump spent the weekend at the White House.
Kelly, who was Trump's chief of staff when the House Republicans lost their majority in the midterm elections this year, said he had made clear to the president that the "last thing" he needed was a political aide in that job.
CenturyLink outage affects 911 phone service
Jessica Rosenworcel, a member of the Federal Communications Commission, said via Twitter her agency needed to investigate. The 911 outage did not affect Snohomish or Whatcom counties, according to the call centers' social-media posts .
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.
"It's never been: The president just wants to make a decision based on no knowledge and ignorance", Kelly avowed, adding that, "You may not like his decision, but at least he was fully informed on the impact". The White House has dropped its request further to $2.5 billion, but Democrats are holding the line against funding the wall.
Mr Trump earlier had upped the brinkmanship by threatening anew to close the border with Mexico to press Congress to cave to his demand for money to pay for a wall.
Mr Kelly will leave the White House on Wednesday after 17 months.
Republican Sen. Lindsey Graham of SC says President Donald Trump is open-minded about combining wall funding with other things to end a partial government shutdown.
Graham said that while the president had not committed to the deal proposal, it was the "outline of a potential breakthrough".
Mulvaney: Pelosi stalling shutdown talks over House speaker bid
The shutdown is now likely to last into the new year when Democrats will retake control of the House of Representatives. The Senate bill contains $1.3 billion for border security excluding any concrete wall.
There's little indication of any imminent agreement to resolve the standoff before the new Congress convenes on January 3.Trump is demanding $5 billion for the wall, while Democratic leaders proposed $1.3 billion for border security. "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 when it comes to the drugs pouring in".
Meanwhile, neither side appeared ready to budge off their negotiating positions. But a previous attempt to reach a compromise that addressed the status of Dreamers broke down a year ago as a result of escalating White House demands. "Now is a good time to fold in some way ... because once Democrats take control of the House, he is going to have a very losing hand". Now Democratic leaders are adamant that they will not authorize money for the project, calling it wasteful and ineffective.
White House counselor Kellyanne Conway on Sunday defended President Donald Trump's border security rhetoric - including the assertion that "any deaths of children" at the border are "strictly the fault of the Democrats" - after a second migrant child died in United States custody earlier this month.
The House and Senate gaveled in and out of session in under five minutes on Thursday.
The shutdown is forcing hundreds of thousands of federal workers and contractors to stay home or work without pay. "Now we have to do it the hard way, with a Shutdown".
President, first lady visit Iraq in first trip to troubled region
While you were stuffing your face with Aunt Cathy's holiday pudding, Trump and Melania chose to visit the troops in Iraq . I'm sure we'll be hearing about it if he said anything to question the existence of Santa Claus during his visit.
The inaction would extend the shutdown into the New Year and into the hands of the new Democratic-controlled House of Representatives. "I'm surprised that the Democrats are this lax on the wall".