WASHINGTON (Reuters) - The two top Democrats in the U.S. Congress sent mixed signals on Monday about chances for cutting a deal with Republicans to save the “Dreamer” immigrants from deportation and preventing a federal government shutdown ahead of a Jan. 19 deadline.

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Nancy Pelosi, leader of the Democrats in the House of Representatives, held out hope for a bipartisan agreement this month. Senate Democratic leader Chuck Schumer also said a deal was possible, but accused the White House of making “unreasonable” demands on immigration.

“Hopefully we could come to some agreement within the next week,” Pelosi told a small group of reporters in her office.

Congress and the White House have been locked in talks on spending and immigration. If they do not make a deal by Jan. 19, when current government spending authority expires, a partial shutdown of the government could follow.

Schumer said on the Senate floor that, following an encouraging meeting last week, the White House has issued “a series of unreasonable demands,” including calling for $18 billion to fund construction of a wall along the southwestern border with Mexico.

Republican President Donald Trump also wants to pump up military spending in the fiscal year that began Oct. 1. Democrats want any Pentagon spending increase to go with more money for non-defense programs, some of which have been capped.

Republicans have majorities in both chambers of Congress, but Democrats are needed to get spending bills past procedural hurdles in the Senate.

Democrats want to protect undocumented people who immigrated illegally into the United States as children, known as “Dreamers.” Trump in September said he was terminating the Deferred Action for Childhood Arrivals (DACA) program and challenged Congress to come up with legislation to protect around 700,000 “Dreamers” from deportation.

Pelosi said on Monday the budget and DACA issues were linked. “We won’t sign off on DACA until we have a caps deal,” she said.

But she added: “I think the opportunity is there. I do think the president sincerely would like to deal with DACA. I think ... a large number of Republicans would vote for a DACA agreement.”