Senate Majority Leader Mitch McConnell, R-Kentucky, announced plans to vote at 1 a.m. Monday on a three-week continuing resolution to fund the government after a day of lawmakers playing the blame game on Capitol Hill for the shutdown. The Senate adjourned Saturday evening and will reconvene Sunday and "as long as it takes."

Negotiations appeared virtually stalled on Capitol Hill late Saturday, as Republicans and Democrats hold firm to their positions after a government shutdown went into effect Saturday at midnight.

Leaders in both parties are blaming each other for the shutdown, holding press conferences and giving speeches throughout the day. Republicans are framing it as a "Schumer shutdown," while Democrats are calling it a "Trump shutdown."

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At the White House, dialing the main number got a recording that blames Democrats for holding national security hostage, and that recording promises someone will pick up the phone -- but not until the shutdown ends, CBS News' Major Garrett reports.

McConnell asked for unanimous consent to begin consideration of a three-week spending bill — shorter than the four-week spending bill the Senate failed to vote on Friday night — but Sen. Ron Wyden, D-Oregon, rejected that move, continuing the shutdown. McConnell objected to a measure from Sen. Ben Cardin, D-Maryland, to continue paying federal workers during the shutdown. In the House, disagreement became so intense that when Republicans attempted to use a poster of Schumer as a prop, Democrats objected and the Senate held a vote on whether Republicans could use the poster.

Marc Short, director of White House legislative affairs, asked when he thinks a vote will be, said, "I think tomorrow. That's my thinking." But his guess is probably as good as anyone's, as Saturday draws to a close. As the sun set on Washington on Mr. Trump's inauguration anniversary, the president tweeted there is "unprecedented success" for our country.

Unprecedented success for our Country, in so many ways, since the Election. Record Stock Market, Strong on Military, Crime, Borders, & ISIS, Judicial Strength & Numbers, Lowest Unemployment for Women & ALL, Massive Tax Cuts, end of Individual Mandate - and so much more. Big 2018! — Donald J. Trump (@realDonaldTrump) January 20, 2018

Short told reporters Saturday in a White House briefing that Democrats shut down the government because the Trump administration accomplished too much in its first year. Short said earlier in the day the White House would not be open to discussing fixes to the Deferred Action for Childhood Arrivals (DACA) program while the government is shutdown. Meanwhile, Democrats are determined to find an immigration fix, with time running out before the program's protections end March 5.

"They look at the accomplishments of the last year, and all this administration has accomplished, and their reaction is, because we can't beat them, we're going to shut down the government," Short told reporters.

The National Park Service made announcements Saturday that parks would be unmanned, or closed, due to the lapse in funding. The Statue of Liberty was included in that. A handful of members of Congress, including Rep. Mia Love, R-Utah, and Barbara Comstock, R-Virginia, said they are forfeiting their pay for the remainder of the shutdown.

Mr. Trump, who has not made a public appearance other than through tweets since the shutdown, has officially canceled his scheduled trip to Mar-a-Lago, where he was supposed to celebrate his first year in office with a party that cost $100,000 per couple to attend. "This is the One Year Anniversary of my Presidency and the Democrats wanted to give me a nice present. #DemocratShutdown," the president tweeted early Saturday morning.

The president, who has been relatively quiet and made no public appearances outside of tweeting, has been speaking to members of his own party, including McConnell. But the White House called a travel and photo lid shortly after 4 p.m., meaning the White House expects no more activity on its end Saturday. Republican Sen. Jeff Flake, R-Arizona, asked by reporters what he'd heard from the president that day, said, nothing.

Schumer blamed Mr. Trump in a Saturday afternoon press conference, saying the president kept shifting his positions on what he wanted out of a deal, and what he would agree to in the final hours before the shutdown.

"Negotiating with this White House is like negotiating with Jell-O. It's impossible," Schumer said.

Schumer said it's "next to impossible to strike a deal with the president because he can't stick to the terms. I have found this out. Leader McConnell has found this out. Speaker Ryan has found this out."

But Office of Management and Budget Director Mick Mulvaney, in the White House briefing with Short, said Schumer wasn't entirely truthful in his depiction of conversations with the president, suggesting he wasn't willing to offer much border wall funding at all. Mulvaney's office is responsible for implementing logistics in the shutdown. "In fact I found out for the first time last night that the person who technically shuts down the government is me, which is kind of cool," Mulvaney said on Sean Hannity's radio show Friday.

House Minority Leader Nancy Pelosi and other House Democrats held a post-caucus meeting press conference late Saturday morning, hours after the Senate failed to reach an agreement on government funding Friday night, triggering a partial shutdown.

"He promised infrastructure, he gave us a train wreck," Pelosi said of Mr. Trump, on the one-year anniversary of his inauguration, noting what she saw as broken promises from the commander-in-chief.

Republicans are trying to convince the Democratic counterparts, CBS News' Nancy Cordes reports, to agree to a three-week spending deal, instead of the previous 30-day proposal. Republicans insist on saving immigration, specifically DACA, for once the government is back and running.

"There is a deal out there to be made," House Freedom Caucus Chairman Mark Meadows, R-North Carolina, told CBSN Saturday afternoon, talking about immigration. "I'm willing to engage. the president is willing to engage. All we need to do is open this government back up and get to a solution in the coming weeks."

But Democrats fear a slightly shorter spending agreement would make no difference. Congress has been divided on spending matters since Mr. Trump in September announced he would be ending DACA.

A deal on spending and immigration seemed possible last week, when Mr. Trump met with both Republicans and Democrats in congressional leadership at the White House. Mr. Trump said he would be open to a clean bill to fix DACA, then seemingly shifted his position shortly after, saying he wants border security funding and funding for the border wall to be a part of any immigration-related bill.

Schumer said he told the president he would even consider border wall funding on the table. A deal, Schumer said, seemed more possible. But then, according to Schumer, the president called him and said he heard Congress had reached a deal to fund the government for three weeks. It had not — the idea was merely that, an idea floated by a handful of Republicans. But then, Mr. Trump began adding more requirements for any such deal, Schumer said, making a spending deal less of a compromise and more of a capitulation to immigration hardliners.

As of Saturday evening, there is no tangible alternative proposal to fund the government.

— CBS News' Kathryn Watson, Alan He and Nancy Cordes contributed to this post