Without Democrats, House Speaker Paul Ryan, R-Wis., is counting on his rank-and-file - including the House Freedom Caucus - to help keep government's doors open.
Trump and Congress are facing a deadline of Friday at midnight to pass fresh spending legislation.
House Minority Leader Nancy Pelosi, D-Calif., said Thursday that Democrats would not vote for the two-week continuing resolution to fund the government.
Trump has a meeting with senior leaders of both parties at the White House on Thursday to discuss a long-term spending bill that incorporates measures both sides want.
The president expressed confidence that congressional Republicans would reach a bicameral agreement on taxes soon.
He says: "We're all here as a very friendly, well-unified group". "It's a well-knit together group of people", Trump said.
Perhaps the strangest reason to believe that a shutdown could be imminent is that Trump seems to think that a shutdown would be good for him politically, and that the blame would fall on Democrats.
This meeting is a make-up of sorts.
President Donald Trump escalated the conflict and implied the possibility of a shutdown when he tweeted about Senator Chuck Schumer and Representative Nancy Pelosi last week, accusing them of obstructing a budget in order to push for immigration reform, which he claimed would result in "flooding our Country" with "illegal immigrants".
"We're here in the spirit of 'let's get it done, '" Schumer said in the Oval Office on Thursday. "There's nothing about veterans' funding, nothing about CHIP- CHIP - children's health insurance, community health centers, nothing about, well, the DREAM Act, among other things", she said. Conservative Republicans said on Tuesday they would try to pass temporary spending bills without House Democrats' support.
Democrats have a rare chance to win major concessions in a US Congress they do not control by taking advantage of a battle within the Republican Party over keeping the government open. That would give bargainers time to work through their disagreements, but they will need Democratic votes to succeed.
'The Democrats are really looking at something that is very risky for our country.
Trump on Wednesday ignored Democrats' pleas to include a measure saving the Deferred Action for Childhood Arrivals program that he axed with a six-month delay earlier this year on the basis that it was an unconstitutional executive action by the previous administration. If they cannot agree on the terms, parts of the federal government could shut down. Trump repealed DACA in September, ending the program that protects young immigrants who were brought to the USA illegally as children from deportation. DACA keeps those almost 700,000 immigrants from being deported by immigration authorities.
Democratic votes for any budget measure will be crucial in the Senate, where Republicans by themselves lack the 60 votes needed to approve the legislation.
As a condition of backing new spending, many Democrats have demanded legislative protections for the almost 700,000 undocumented immigrants who were brought into the United States as children.
Republicans have demands, too. In a deal to raise the limits, defense hawks want a sizable increase in military spending. Republicans generally favor more money for defense programs, while Democrats often demand equal increases for domestic social programs. "The number one priority for our country is to make certain we protect this Constitution and our way of life, and we've got great bipartisan support".
The White House says the leaders were taken to the Situation Room for a briefing by Mattis on military matters.
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