Democrats have leverage because a bill needs 60 votes in the Senate to pass.
Despite Trump's rhetoric, some lawmakers are downplaying the possibility of a government shutdown.
The top Democratic lawmakers, Senate Minority Leader Charles Schumer and House Minority Leader Nancy Pelosi, boycotted White House spending talks a week ago after Trump, a Republican, said he did not see a deal in the offing.
To jumpstart that negotiating, Trump and congressional leaders agreed to meet Thursday an attempt to reach agreements.
"We're all here as a very friendly, well-unified group".
"It could happen", Trump said about a shutdown. "We want to have a great, attractive crime-free country".
This meeting is a make-up of sorts.
His remarks before a Cabinet meeting drew a tweet from House Minority Leader Nancy Pelosi, D-Calif.
"We're here in the spirit of 'let's get it done, '" Schumer said in the Oval Office on Thursday.
The Republican-controlled House is expected to vote on Thursday on a bill that would keep the government open at current spending levels through December 22 while lawmakers negotiate a longer-term solution.
Pelosi has echoed the sentiment, and said last week "we want to keep government open".
In October 2013, conservative Republicans used the need to pass a funding bill to try to force repeal of the Affordable Care Act, also known as Obamacare. That would give bargainers time to work through their disagreements, but they will need Democratic votes to succeed. If they cannot agree on the terms, parts of the federal government could shut down. Those are the roughly 700,000 immigrants in the country illegally who were brought to the U.S.as children. DACA keeps those almost 700,000 immigrants from being deported by immigration authorities.
Trump has given Congress until March to resolve the issue, with Democrats wanting to vote now, and Republicans mostly hoping to put off any immigration vote until next year after approving the tax and budget legislation.
President Donald Trump said Wednesday that a government shutdown "could happen" and it will be Democrats' fault if it does.
Democrats have opposed his plan to build a wall along the border with Mexico, but have expressed a willingness to fund other border security measures.
"The reality is that we're running into a deadline this week, and this resolution is our best and only option at this time", said Representative Rodney Frelinghuysen, Republican of New Jersey and the chairman of the House Appropriations Committee.
The legislation will include some short-term help for states running out of money to finance a health insurance program for lower-income children.
Pelosi said the temporary spending measure before the House on Thursday was a "waste of time".
Republicans have demands, too.
The group is set to discuss a potential deal to raise defense and non-defense budget caps.
Trump's warning about a shutdown came as conservative House members pushed for increases in military spending along with either a freeze or reduction in domestic programs. Democrats have a history of strongly supporting stopgap funding bills, providing the cushion for victory in the Republican House.
The Wisconsin Republican says, "I feel good where we are".
Press Secretary Sarah Sanders said Thursday that the leadership was "receiving an update on our military by Secretary of Defense Jim Mattis".