By Siobhan Hughes, Kristina Peterson and Natalie Andrews 

WASHINGTON -- Republicans and Democrats in the House and Senate dug into their positions in a fight over immigration policy Saturday, as leaders from both parties tried to gain the upper hand by blaming one another for a spending impasse that triggered the first government shutdown in more than four years.

President Donald Trump called Senate Majority Leader Mitch McConnell, according to a White House aide, who said the Kentucky Republican was expected to put forth a new three-week spending bill as part of a broader plan to break a deadlock that has been building for months.

In the House, Republican leaders were preparing a multipronged approach, and were ready to vote on a new spending bill if one passes the Senate but also weighing their own new offer.

Funding for the government expired at 12:01 a.m. ET Saturday after the Senate rejected a one-month spending bill that had earlier been passed by the House. Despite the shutdown, much of the federal government's work was expected to continue, as some departments' operations are deemed essential and some agencies say they have sufficient funds to carry on operations for a few days, while lawmakers sort out their differences

The impasse set off a new round of finger-pointing that continued into Saturday.

Many House Republicans came back to the Capitol Saturday morning with a renewed determination to pass a spending bill free of any immigration-related policy changes, convinced that Democratic resolve would weaken.

In a closed-door House GOP conference meeting, Speaker Paul Ryan (R., Wis.) read out headlines from the morning's newspapers that he said indicated Senate Democrats were responsible for the shutdown, according to a person in the room.

Mr. Ryan told cheering GOP lawmakers that Republicans had been reasonable while Democrats had overreached and that the minority party was now seeking a way out.

Later, on the House floor, Mr. Ryan said "the federal government is needlessly shut down because of Senate Democrats."

"One party in one house of this Congress is deliberately holding our government hostage. This did not need to happen," Mr. Ryan said.

Mr. McConnell, on the Senate floor, echoed that sentiment.

"Like the president, like the House and like a bipartisan majority of senators, the American people cannot begin to understand why the senate Democratic leader thinks the entire government should be shut down until he gets his way on illegal immigration," Mr. McConnell said, referring to Senate Minority Leader Chuck Schumer (D., N.Y.) "The solution is to end the foolishness that's hurting millions of Americans who've done absolutely nothing to deserve this."

Democrats said their resolve to find a solution to the immigration issue wasn't weakening and said the party that controls the White House and Congress are responsible.

"We are happy and eager to compromise, but we will not be bullied," Mr. Schumer said on the Senate floor. "The Republicans control the White House, the Senate, the House. That's why America and the world are calling this shutdown the Trump shutdown." Mr. Schumer said that Mr. Trump has "turned blowing up bipartisan agreements into an art form."

"Negotiating with President Trump is like negotiating with Jello," Mr. Schumer said.

At the White House, the president was receiving regular updates and spoke with both Mr. McConnell and Mr. Ryan, spokeswoman Sarah Huckabee Sanders said. "We are committed to making sure the American people, especially our great military and the most vulnerable children are taken care of," she said. "The President will not negotiate on immigration reform until Democrats stop playing games and reopen the government."

The shutdown marked the culmination of a fight that began in September, when Mr. Trump ended a program shielding the young illegal immigrants known as Dreamers from deportation. He gave Congress until March 5 to hash out a replacement.

Democrats had hoped to use their leverage in the Senate, where Republicans control 51 seats but need 60 votes to pass the spending legislation, to force Republicans to agree to legal protections for the Dreamers. But Mr. McConnell said he wouldn't hold a vote on a deal not blessed by Mr. Trump and that Democrats shouldn't be tying government operations to the immigration fight.

Mr. Trump, on Twitter early Saturday morning, accused Democrats of being "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!"

His legislative director, Marc Short, on Capitol Hill for meetings with Republicans, told reporters Saturday that the White House was "actively fighting to make sure the government stays open," planning to flood Congress with a new round of phone calls. Mr. Short also rejected an immigration measure from a bipartisan group in the Senate led by Lindsey Graham (R., S.C.) and Dick Durbin (D., Ill.) that is part of a conversation in the chamber about a path forward to reopening the government.

That legislation would extend legal status to Dreamers, providing them with a 10-12 year path to citizenship. It would also provide about $2.7 billion for border security and operations, end the diversity visa lottery, which randomly awards 50,000 green cards to would-be immigrants from underrepresented countries, and eliminate the ability of legal permanent residents to sponsor adult children for green cards.

"We're pleased that the proposal actually focused on the four areas we're interested in, but it's woefully insufficient," Mr. Short said. He said that "we're anxious to get a bill to the floor that the president can sign. That one is not one that he can sign."

How that stance plays out in the Senate is an open question. Mr. Graham said in a statement Saturday that he believes a measure to fund the government through Feb. 8 would pass the Senate it GOP leaders also committed to vote on immigration legislation if no alternative agreement was reached with the White House and the House. Under such a deal, senators would be allowed amendment votes, an option that leaders don't always allow.

But Senate Democrats have balked at considering immigration legislation unless it is attached to a must-pass measure.

Mr. McCarthy told reporters that he thought a spending bill to fund the government through Feb. 8 would pass the House. But Republican leaders were also discussing other options.

House Rules Committee Chairman Pete Sessions (R., Texas), who manages the committee through which all legislation must move before going to the floor, said he would "anticipate that we would have an offense, not a defense," meaning a new proposal to offer the Senate.

Republicans were convinced that Senate Democrats had overplayed their hand and were looking for a way out. "Inside the Democratic conference, they are not happy about this," House Majority Leader Kevin McCarthy (R., Calif.) said, adding that he had been texting with Democrats. "This is irresponsible. "It's almost like a tantrum....you have to do everything that I want -- otherwise everybody else has to be hurt.

The Senate was expected to be back in session at noon, while House lawmakers returned to work for a 9 a.m. session.

Mr. Trump on Friday had canceled plans to travel to his private resort on Palm Beach, Fla., where an event had been planned for Saturday to celebrate the anniversary of his first year in office.

The Saturday sessions follow a dramatic night of intense negotiations, and a failed 50-49 Senate vote to move forward with a House bill that would have funded the government through Feb. 16.

Five Democrats voted with most Republicans for the bill while five Republicans opposed it, including Mr. McConnell, a move that allowed him to bring it up for another vote later. Sen. John McCain (R., Ariz.) didn't vote because he was at home undergoing cancer treatment.

Much of the government's work is expected to continue despite the shutdown, as the Trump administration aims to apply what senior administration officials called flexibility to shutdown rules that contain a variety of exceptions.

Mr. Trump's own activities, including planned travel to the World Economic Forum in Davos, Switzerland, can continue under an exemption for activity required by the president to carry out his constitutional duties.

Lawmakers said early Saturday they weren't sure how this shutdown would compare to the most recent one, in 2013, which lasted 16 full days.

"I cannot think of one that really compares to this," said Vermont Sen. Patrick Leahy, the longest serving Democrat in the Senate. "We've never had an instance where the president changes his mind all the time, and then says we ought to have a good shutdown. I can't think of any president, Republican or Democrat, who wanted a shutdown."

Mr. Trump said on Twitter last May that a government shutdown might be needed to get his priorities through Congress.

Write to Siobhan Hughes at siobhan.hughes@wsj.com, Kristina Peterson at kristina.peterson@wsj.com and Natalie Andrews at Natalie.Andrews@wsj.com

(END) Dow Jones Newswires

January 20, 2018 14:15 ET (19:15 GMT)