Washington • Congressional leaders in both parties refused to budge publicly from their political corners Saturday on the first day of the government shutdown, avoiding direct negotiations and bitterly blaming each other for the impasse in speeches. President Trump joined the fray with a series of charged tweets.

But private glimmers of a breakthrough were evident by late Saturday, as moderate Democrats and Republicans began to rally behind a new short-term funding proposal to reopen the government through early February.

That plan could include funding for storm-ravaged states, reauthorization of the Children’s Health Insurance Program — and an implicit agreement to hold votes at some point in the coming weeks on a bipartisan immigration deal, according to senators involved in the discussions.

Senate Majority Leader Mitch McConnell, R-Ky., vowed on the Senate floor late Saturday to take up a new spending plan by Monday morning, or sooner, that would keep government open through Feb. 8 but would not contain a solution for “dreamers,” undocumented immigrants who were brought into the country as children.

“He wants to keep the government shut down until we finish a negotiation on the subject of illegal immigation,” McConnell said of his Democratic counterpart, Senate Minority Leader Charles Schumer, D-N.Y. McConnell then repeated himself: “Shutting down government over illegal immigration.”

The moderate senators, meanwhile, are trying to reach a deal on immigration in hopes that, after the three-week spending deal is approved, McConnell would allow it to come up for a vote alongside a longer-term spending plan.

Democrats, however, remained intensely opposed to a short-term spending measure, frustrated by Republicans’ refusal to meet their demands on immigration while government is closed. At issue for Democrats is the fate of thousands of young immigrants eligible for protection from deportation under the Obama-era Deferred Action for Childhood Arrivals program. Trump canceled the program in September, and it is set to expire in March. Lawmakers are scrambling to enact a legislative solution.

Democrats also questioned the ability of the negotiating group to reach an agreement that can pass the Senate and House and also earn Trump’s approval.

“The conversation that needs to take place is the conversation at 1600 Pennsylvania Avenue, where the president of the United States brings in the four leaders from Congress,” said Sen. Thomas Carper, D-Del. “We can come up with the best compromise in the world. The key is how to get it through the House and the way to do that is for the president to provide the air cover that he has not so far provided.”

Lawmakers in both chambers were scheduled to return to work Sunday afternoon.

McConnell and Schumer did little in public Saturday besides trade insults in brief speeches on the Senate floor or on television.

“Do you know what number CR this is? This has been going on for six months,” Schumer told CNN, using the legislative term for a short-term spending deal, a continuing resolution. “This is the fourth time. They can’t get it done and they just use these CRs.”

McConnell hunkered down in his office and played phone tag most of the day with Trump, updating him on where things stood and projecting an air of confidence that he was in a strong position, according to GOP senators.

There were no substantive talks between Schumer and McConnell. The real effort at bridging the divide was a bipartisan collection of roughly 20 senators from the less ideological corners of their respective caucuses. That group met and was trying to advance deal that would open the government for three more weeks and set up a series of votes on competing immigration proposals. However, several Senate Republicans said that McConnell was in no mood to give Schumer any assurances to open up the government.

Sen. Susan Collins, R-Maine, and Sen. Joe Manchin III, D-W.Va., are leading the moderate group, with Sens. Jeff Flake, R-Ariz., and Lindsey Graham, R-S.C., both of whom have worked closely with Schumer on immigration issues in the past, serving as go-betweens for the two parties. The duo shuttled back and forth between Schumer’s and McConnell’s offices on the second floor of the Capitol trying to create peace, but they left for dinner shortly after 6 p.m. with no solid agreement with either leader.

It’s unclear whether there is enough bipartisan support for the immigration proposal being offered by Flake and Graham — or for one that Senate conservatives are also drafting. One danger for everyone involved: the possibility of no resolution to the immigration standoff three weeks from now, leaving Congress and Trump back in the same spot where they are now.

So far, Trump, McConnell and House Speaker Paul Ryan, R-Wis., have refused to consider Democrats’ demands until there is a bipartisan agreement to reopen the federal government.

“Senate Democrats shut down this government, and now Senate Democrats need to open this government back up,” Ryan said in a midday speech.

And Trump weighed in on Twitter: “Democrats are far more concerned with Illegal Immigrants than they are with our great Military or Safety at our dangerous Southern Border. They could have easily made a deal but decided to play Shutdown politics instead. #WeNeedMoreRepublicansIn18 in order to power through mess!”

Saturday marked the straight day that the moderate senators had hunkered down in Collins’ office. Collins led a similar bipartisan group in working to resolve the last shutdown in 2013.

Moderates are “trying to find a pathway forward,” Manchin said.

Democratic leaders, meanwhile, made their case for blaming Republicans for the shutdown. As thousands of women gathered along the Mall in Washington to protest Trump’s first year in office, House Minority Leader Nancy Pelosi, D-Calif., stood at a news conference at the Capitol pointing at a poster depecting a Trump tweet from last May calling for a “good shutdown.”

“Happy Anniversary, Mr. President,” Pelosi said. “Your wish came true. You wanted the shutdown? The shutdown is all yours.”

Trump, who marked the first anniversary of his inauguration on Saturday, canceled plans to visit his resort Palm Beach, Florida, for a weekend of celebrations. His scheduled trip to the World Economic Forum in Switzerland this coming week was also up in the air, according to an aide.

At the White House, a phone line for comments directed callers to voicemail with a message slamming Democrats.

“Unfortunately, we cannot answer your call today because congressional Democrats are holding government funding, including funding for our troops and other national security priorities, hostage to an unrelated immigration debate. Due to this obstruction, the government is shut down,” a woman’s voice said on the message.

The White House said it supports the Feb. 8 plan, eliminating a potentially significant hurdle to its enactment. But simmering tensions between Trump aides and Schumer, who said Saturday that negotiating with the president was like negotiating with “Jell-O,” underscored the delicacy of the moment.

Schumer and Trump had met privately on Friday afternoon, giving some lawmakers hope their discussion would advance a deal to avoid a shutdown altogether.

Schumer left the meeting buoyed, telling others that Trump seemed willing to strike a deal on a days-long funding extension in exchange for concessions such as border wall funding. But by midnight, he complained to his members that Trump had suddenly reneged on the possibility.

The White House told a different story. Briefing reporters at the White House on Saturday, budget director Mick Mulvaney disputed Schumer’s claim that he offered Trump his desired border wall funding during their meeting.

“Mr. Schumer has to up his game and be more honest with the president of the United States if we are going to be seeing progress,” Mulvaney said.

Schumer spokesman Matt House fired back on Twitter that Mulvaney was not present for the meeting was “not telling the truth” about what happened.

Democrats pushed for a shutdown to spite Trump for his accomplishments, White House Director of Legislative Affairs Marc Short argued to reporters.

“Their reaction is, ‘Because we can’t beat them, what we’re going to do is shut down the government,” he said in a news briefing Saturday.

There was little productive activity on the House and Senate floors.

McConnell sought to bring up the four-week spending bill that failed Friday night; Democrats blocked the attempt. Democrats asked to vote on a bill guaranteeing federal workers their back pay for the period of the shutdown; McConnell objected, saying they deserve a full funding bill.

Sen. Ron Wyden, D-Ore., the ranking member of the Senate Finance Committee who objected to McConnell’s attempt to revive the short-term bill, questioned McConnell’s embrace of the GOP proposal to extend funding of the Children’s Health Insurance Program.

“He sounded like Marian Wright Edelman last night, the founder of the Children’s’ Defense Fund, with his newfound interest in the children’s’ health plan,” Wyden said in an interview. “It sounds like I’m listening to Ted Kennedy talk about health. ... I’ve never heard of this being a priority [for Republicans].”

In the House, lawmakers prepared for a possible deal by debating a special rule allowing them to consider any bill that passes the Senate on the same day. The debate devolved into a shouting match over displaying disparaging photos of other members — such as Schumer — on the floor.

The Washington Post’s Elise Viebeck and Juliet Eilperin contributed to this report.