(AFP) - Donald Trump's first anniversary as US president was marred by chaos Saturday as lawmakers traded bitter recriminations over a government shutdown while mass demonstrations erupted in cities across the country.

The famed Statue of Liberty was among the federal sites that were shuttered on Saturday. But the real impact of the shutdown won't be fully felt until Monday morning, when hundreds of thousands of public sector workers are set to stay home without pay.

Top Senate Republican Mitch McConnell on Saturday night tried to head off that possibility, setting a key vote for a funding measure for 1:00 am (0600 GMT) Monday.

"I assure you we will have the vote at 1:00 am on Monday, unless there is a desire to have it sooner," he said in a statement.

Highlighting the deep political polarization, crowds estimated to number in the hundreds of thousands took to the streets of major US cities to march against the president and his policies.

"This is the One Year Anniversary of my Presidency and the Democrats wanted to give me a nice present," Trump, who is in Washington instead of celebrating at his Mar-a-Lago resort as originally planned, wrote on Twitter in reference to the shutdown.

"Democrats are far more concerned with Illegal Immigrants than they are with our great Military or Safety at our dangerous Southern Border," he tweeted, later accusing the opposition party of "holding our Military hostage."

The impact of the shutdown would be felt acutely if it lasts into the coming work week.

Essential federal services and military activity are continuing, but even active duty troops will not be paid until a deal is reached to reopen the US government.

- 'Holding pattern' -

There have been four government shutdowns since 1990. In the last one in 2013, more than 800,000 government workers were put on temporary leave.

"We're just in a holding pattern. We just have to wait and see. It's scary," Noelle Joll, a 50-year-old furloughed US government employee, told AFP in Washington.

Joll was also affected by the 2013 shutdown, but "this one feels a lot more ominous," she said.

A deal had appeared likely on Friday afternoon, when Trump -- who has touted himself as a master negotiator -- seemed to be close to an agreement with Democratic Senate minority leader Chuck Schumer on a measure to prevent the expulsion of undocumented migrants who arrived in the United States as children.

But no such compromise was in the language that reached Congress for a stop-gap motion to keep the government open for four more weeks while a final arrangement is discussed. And Republicans failed to win enough Democratic support to bring it to a vote.

Congress reconvened for a rare Saturday session, where leaders of both sides were meant to hammer out their differences to prevent the shutdown from stretching into Monday. Instead, they traded accusations of responsibility for the shutdown.

Schumer said trying to negotiate with Trump "was like negotiating with Jell-O."

"It's impossible to negotiate with a constantly moving target," he said. "President Trump is so mercurial it's been impossible to get him to agree to anything."

Meanwhile, McConnell said Schumer "took the extraordinary step" of preventing the legislation from passing and thus "plunging the country into this totally avoidable mess."

"We're dysfunctional right now," said Democratic Senator Joe Manchin, who voted in favor of the funding measure on Friday night.

"If we can't open the government back up and work through our differences, it would be a travesty."

"Tomorrow this should come to an end. The true, unacceptable silliness that we go through must stop."

- Anti-Trump protests -

Democrats have accused Republicans of poisoning chances of a deal and pandering to Trump's populist base by refusing to fund a program that protects 700,000 "Dreamers" -- undocumented immigrants who arrived as children -- from deportation.

Republicans have a tenuous one-seat majority in the Senate, but on Friday needed to lure some Democrats to their side to get a 60 vote supermajority to bring the motion forward. They fell ten votes short.

The measure brought to Congress would have extended federal funding until February 16 and reauthorized for six years a health insurance program for poor children -- a long-time Democratic objective.

But it left out any action on the Deferred Action on Childhood Arrivals program, known as DACA, that affects Dreamers.

White House officials insisted there was no urgency to fix DACA, which expires March 5.

As US lawmakers wrangled over government funding, protesters turned out in cities including Los Angeles, New York and Washington to express their opposition to Trump, and their support for women's rights.

Protestors hoisted placards with messages including "Fight like a girl" and "A woman's place is in the White House" and "Elect a clown, expect a circus."

The president meanwhile posted a deadpan tweet referencing the rallies protesting his policies, urging people to "get out there and celebrate the historic milestones and unprecedented economic success and wealth creation that has taken place over the last 12 months."

Later Saturday, he tweeted again about the "unprecedented success for our Country, in so many ways, since the Election."

Hollywood celebrities were among those who turned out to the protests.

"We have a racist in the White House, we have a sexist in the White House and we have a pathological liar in the White House who is tearing away at the fabric of our democracy," actor and producer Rob Reiner said at a rally in California.

© Agence France-Presse