In an extended interview with the LA Times, Kelly told reporters that the President routinely consults multiple sources of information before making a decision, even if it often seems like Trump acts without regard for consequences.
At present it is still unclear if Congress will allow funding for Mr Trump's desired border wall.
In his almost two years in office, Mr Trump has fired or forced out six Cabinet officials, shuffled two others into different posts and seen the most high-profile woman in his administration announce her resignation.
The comments come amid the third U.S. federal government shutdown in 2018, as Congress has refused to allow the $7 billion to fund Mr Trump's proposed border wall with Mexico.
The threat comes one week after a deadlock in Washington over the federal budget caused a partial shutdown of the United States government.
Trump spoke about the wall funding fight during his visit to US troops in Iraq on Wednesday, but he has not made a public statement about it since he returned, other than on Twitter.
"Jeb Bush just talked about my border proposal to build a "fence", he tweeted. "And negotiation by definition has to include both sides".
In a tweet Saturday, Trump said Democrats should take the initiative on ending the shutdown, saying, "I am in the White House waiting for the Democrats to come on over and make a deal" on border security.
She added: "It really depends on what Customs and Border Patrol says they need". Senate Democratic leader Chuck Schumer told Vice-President Mike Pence that it wasn't acceptable, nor was it guaranteed that Trump, under intense pressure from his conservative base to fulfil his signature campaign promise, would settle for that amount.
Since then Trump's aides have claimed that Democrats have abandoned the negotiating table, while Democrats assert that the president's administration have not contacted Pelosi directly in weeks, reported Associated Press.
NAFTA, the North American Free Trade Agreement, effective since New Year's Day in 1994, was created to increase trade among the U.S., Canada and Mexico.
Democrats have offered support for $1.3 billion in funding for general border security, but have long opposed the building of a wall.
Graham, R-S.C., told CNN State of the Union host Dana Bash he believes a deal that would provide the $5 billion of funding for border security in the form of a wall or other barrier and a three-year one-time renewable work permit for about 70,000 people under the Deferred Action for Childhood Arrivals program "might save the day in the Senate".
"The president would ask things like, "'Why can't we do it this way?'" Kelly said. "Meanwhile, the president tweets blaming everyone but himself for a shutdown he called for more than 25 times".
Trump was cooped up in the White House after cancelling a vacation to his private Florida club. "So we fully expect that until she is elected speaker and has locked that vote up, we don't expect to hear from the Democrats again", Mulvaney continued. The inaction would extend the shutdown into the New Year and into the hands of the new Democratic-controlled House of Representatives.
"We will be forced to close the Southern Border entirely if the Obstructionist Democrats do not give us the money to finish the Wall & also change the ridiculous immigration laws that our Country is saddled with", the president wrote in the first of a December 28 battery of tweets.