There is no plan, ' " Trump, 72, tweeted on Saturday, without indicating where he saw the report. Trump has said he'll sign it.
As ever, the proposed border wall between the US and Mexico is the sticking point.
"Democrats could solve the Shutdown in 15 minutes!" he said in one tweet, adding in another, "We will be out for a long time unless the Democrats come back from their "vacations" and get back to work".
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 USA 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.
There's good news for Republicans, though, looking to obtain some sort of immigration reform compromise in ongoing budget negotiations: most wall supporters polled by the Washington Post want Republicans - and especially President Trump - to stand firm on making funding for the border wall part of the final budget package.
Graham said he thinks Trump is willing to accept the level of wall funding he is seeking, along with some immigration measures Democrats might find acceptable, such as helping immigrants who were illegally brought to the U.S.as children.
The record shutdown has furloughed 800,000 federal employees and cut government services across the United States, caused by a lack of agreement between Republicans and Democrats over their funding.
Trump's wall is winning adherents as support increased over the past year.
In addition, 52 percent of respondents said that they did not consider the situation at the US-Mexico border to be a crisis, with only 45 percent describing it as one.
Arizona police collect DNA at nursing home where comatose woman gave birth
Every male employee at a private care facility where a patient in a vegetative state gave birth last month is being DNA tested. San Carlos Apache Police chief Alejandro Benally said Phoenix police "will do all they can to find the perpetrator".
"No, I would do it simultaneously, but I'd like to see them move fast", Trump replied.
The Democrats, newly in control of the House of Representatives, have refused to cite fundamental opposition to Trump's anti-immigrant policies and the proposed wall in particular.
An attempt Thursday by moderate Republican senators to broker a deal that would have traded immigration protections for undocumented "Dreamers" brought to the U.S. as children in return for wall money collapsed after Vice President Mike Pence rejected it. He said the president had accepted a border security package that included money for a wall, then changed his mind.
More Americans-54%-still say they oppose a border wall. Two-thirds of Republicans surveyed would support a move by Trump to declare an emergency to build a border wall, though 66 percent of all respondents said they oppose it. "The president didn't commit but I think he's very open-minded".
Graham favors a declaration and said the time for talk is running out.
The US government shutdown is now the longest such closure in history. "But we need money for that barrier", Trump said.
Some 420,000 federal employees whose work is declared essential are working without pay, including the FBI, TSA and other federal law enforcement officers.
"We don't want it to come down to a national emergency declaration", said House Republican Whip Steve Scalise of Louisiana.